is there a smart way to track the same FoF halo at different redshift? If that's not the case what could be the easiest method?
There are no "FoF merger trees", all the merger trees are based on subhalos.
But the easiest way is simply to go from a FoF to its central subhalo (GroupFirstSub), then load the "main progenitor branch" of that object. Using the SubLink tree, then the fields SnapNum and SubhaloGrNr give you the "FoF merger tree".