Why not shown a selection of available geographic transformations is provided once a Source and Destination Coordinate System are set.

Hi @houxianyong​ ,

Since FME 2012, the Esri has had the ability to

1) Allow ESRI reprojection to use user supplied WKT transformations

2) Allow ESRIReprojector to use custom transformation

As you've noted, these are option and not automatically chosen because some reprojections have transformations available. There is more info that might help to explain the how FME interacts with ESRI coordinate systems.

Why can ArcGIS 10.1 and fme2018 display "geographic transformation" automatically before, but now ArcGIS 10.7.1 and fme2020 can't

How to use custom transformation files (*.gtf files) .I had put it to \\FME\\Reproject\\EsriPEGridData dir,but "geographic transformation" is blank.

Ah I see what you mean @houxianyong​. Our team actually resolved an issue for this recently in FME 2020.1 build 20582. Can you upgrade either the most recent build or the any past build newer than 20582?

Thanks,I have done the experiment。