No. You'll have to create a new file in a new filegroup, then shrink the one you want to remove with the EMPTYFILE option and then drop it. The move the objects that you want in FG4 into that fielgroup.

Files can't move between filegroups because objects are assigned to filegroups and stored in files, if you moved one of the files from FG3 to FG4 you'd suddenly have objects spanning filegroups, which can't happen