I could not find a road access to the core zone of Blue Mountains Jamaica. Car can only enter to the buffer zone. Does anyone know a road? Otherwise we may add this to the no road access connection

I haven't been there, but I think Nanny Falls is included. Google Maps shows a road there.

You are right Els. Nanny Falls locates in the border of the core zone. It still requires some hiking but it is probably in a reasonable length of time.

It's about time for a good review of this WHS

I don't think it does - See this
This shows that the Falls themselves are only reachable by an off road walking trail.
The official map of the site on UNESCO is rather poor - and those in the AB Evaluation/Nomination file are not much better. It does seem from one in the ICOMOS evaluation that the Falls are (might be??) situated "Just" inside a corner of the "Core area" - but, even if they are, I believe that the road and settlements up the Rio Grande Valley up to Moor Town and beyond are all excluded (as are those elsewhere in the NP) - whatever their "Maroon significance".
IUCN eviscerated the original "Mixed" site and refused to allow any non "old forest" areas. ICOMOS "found" enough Maroon heritage in these areas (trails and "sacred sites" etc) to provide cultural OUV .... and Jamaica went along with it - happy enough to get a WHS whatever its size. Most people won't even know that much of the NP and its "Maroon" heritage has been excluded!!
So, I believe that csarica's original "No road" Connection suggestion is correct for this WHS

Thanks for the information, Solivagant. But google maps is not the best for Jamaica.
Can you have a look at the wikimapia.org OSM map?

http://wikimapia.org/#lang=en&lat=18.080896&lon=-76.423259&z=16&m=o

It seems like the car road goes through the border of the core zone.

https://drive.google.com/file/d/1D9Ls9zY66Lo3hEen-3lLJe4nxux8tyP0/view?usp=sharing

I used Google Maps as they were cited above. Agree Wikimapia road version has more detail (though is less good on Terrain versions?) but both agree that no road goes up all the way from Moore Town to Nanny Falls.
See this "Satellite" view of Google maps (you may need to refresh to get that view). Exactly as per Wikimapia, the road continues a bit out of Moore Town beyond "Nanny Falls Tours" and stops at a smallholding well short of the Falls themselves. The route further up to the Falls along the north bank of the river isn't shown as a road on either map in any "view".

So - the issue becomes where exactly the boundary of the Core Zone is in relation to Moore Town, the end of the road and Nanny Falls themselves. All the maps I have found which make any attempt to show this are rather poor and don't zoom well without losing definition. Try the one in the ICOMOS AB evaluation or the Maroon Trail map in the Nomination File on page 24 which both show Nanny Falls as a red dot. You will see another red dot slightly South West which is readable as "Moore Town" (More easily on the Nom File map). If you extrapolate the scale between the 2 dots to derive a distance between them I think you will conclude that the end of the road past "Nanny Falls tours" at the edge of Moore Town doesn't reach the corner of the Core Zone in which Nanny Falls themselves are situated.

And neither would I expect it to - The road stops at the end of "Habitation" and farming and IUCN was determined that the core zone wouldn't include any of these as a matter of principle and deliberately excluded them when drawing the boundaries.

One extra "complexity" is the presence on Google maps of a pin for "Jamaica Tours Eco-retreat Hotel and spa". This would seem to be situated among virgin forest due east of Nanny Falls and also in the core zone. In fact the pin has been placed in entirely the wrong place - the establishment is miles away!!

Another possible "Road" into the core area exists further south along the Rio Grande valley at Ambassadeth Ecolodge (again refresh to Satellite view and see that the place is correctly marked). This is across the border into St Thomas Parish and is situated on the Cunha Pass Maroon Trail. It can be reached by bad road as reviews confirm - but is it in the core zone?? Using the Nom file and ICOMOS evaluation maps again (the former is better) it is clear that the core boundary leaves the parish boundary at exactly this point (having followed it religiously further West) and is situated further south. You will also see a red dot for Hayfield outside the border on the southern side. That location also has a road - but again I would estimate that the core zone boundary has been established to exclude it.

PS 2 points which I have derived from the above "map studies"!!
a. Blue Mountain Peak is NOT within the core zone and the Connection regarding "Territorial Highest points" should be removed for this WHS. See the Trail map referred to above which makes it clear that it is south of the WHS the boundaries. Also looking at the parish boundaries which constitute the NP boundaries - the core zone ends to the north of these all along the ridge
b. The easiest way to visit the core zone is to hike to Nanny Falls from the Moore Town roadhead!!

I've amended the connections & added the No Road Access one.

Also, I have altered the intro text on the site page somewhat, to reflect the remoteness and inaccessibility better.
The photo was taken in or near Holywell, from where trails ("such as the Peak Trail") enter the nominated property.

Update: think I found a road!
See https://www.jcdt.org.jm/images/images-articles/bjcmnp/bjcmnp-overview.jpg
The dark green area is the Preservation Zone of the NP, and corresponds with the WHS core zone.
There is a (yellow) road visible crossing the core zone, north of Hayfield (the same point as indicated by Solivagant above, but I don't think the road is excluded). And according to that map, the peak is also included.

Mmm!?
The Preservation Zone map you have found undoubtedly has 2 yellow (what its legend calls "minor") "roads" crossing the narrowest part of the ridge.
The more westerly down to Hayfield coincides exactly with what is identified in the "Maroon Sites and Trails" map on page 24 of the Nomination File as the "Cuna Cuna Pass Trail" (in Blue) down to Hayfield. The more easterly is identified on the Nom File Map as being the "Corn Puss Gap Trail" (in Green) down to Bath. There is no argument that there are historic crossings of the mountain at both those points, but are the, what are called minor roads on the Zone map, "motorable" for the purposes of our "Connection"??

Here is a description of the "Corn Puss Gap" trail. And here a description of the Cuna Cuna. Note the reference to "Both hikes" starting at Ambassadreth Cabins (Motorable to there - see my earlier post) . The Nom File map clearly shows the starting point south of the Parish border but clearly outside the Core Zone.

The Zone map may have them as "Yellow minor roads" but I do not think there is any evidence that they are motorable. This article (page 10) describes the trails always in terms of them being "hiked"

Regarding the Blue Mountain Peak and whether it is inside the Core Zone or not.
The Preservation Zone map clearly has a black triangle inside the core zone marked "Blue Mountain Peak" - but I am not sure what the big black star to its West and possibly just outside the core zone is meant to be. I personally think that the triangle is too far in from the NP boundary to accurately be the Blue Mountain Peak.
The Maroon Trails map clearly states that Stoddarts trail (in Red) continues beyond the Core boundary to "TO BLUE MOUNTAIN PEAK, PAPINE, AND LIGUANEA"
Which is correct?
There seems no doubt that the core zone in this area runs NORTH of the NP boundary. But by how much??? Less certain (but probable?) is that the NP boundary follows the Parish boundaries. This map on "All Trails" (may require log in but Google log in works) shows that Blue Mountain Peak lies just slightly to the north of the parish boundary. Google Satellite shows the same - but with Google you cant rely on the location of "pins" added by users. I think, looking at the topography on the satellite view, its pin is a bit too far north. So - how much further north than the Parish boundary is the Core Zone boundary??? I really can't decide gien the information at the current time. For the moment do we rely on the Nom File Maroon Trails or the Preservation Zone map?? If you switch to "Satellite view" on the All Trails map it can clearly be seen that there is a "hut" structure at/very near the summit of Blue Mountain Peak (confirmed in reports) together with nearby areas cleared of trees. Was that "enough" for IUCN to run the Core Zone further north??.

I think you are right. I also looked at OpenStreetMap, there you can see better that the road does not fully connect north (Bowden Pen) and south (Hayfield), there's a gap that's a walking trail only. So we keep the No Road Access connection!

Morne Trois Pitons: Suspended cable cars (project)

https://la1ere.francetvinfo.fr/guadeloupe/l-ile-de-la-dominique-accueillera-le-plus-long-telepherique-du-monde-1320196.html

https://www.simagazin.com/en/si-urban-en/worlds-longest-cable-car/