I'm not sure what you mean here. You want to move the physical data? Or the share? Or what?
You should have a filestream/filetable that has a share. something like \\myserver\myshare\
There is then a data folder somewhere, which contains the actual files. This is only referenced by SQL Server. This is usually under your data file, unless you created the filegroup in a different location.
Your data is in a filegroup. You can do a few things.
1. backup/restore , using WITH MOVE to move the filegroup.
2. detach/attach - same thing, move the data folder for the filegroup, attach from a new location
3. create a new filegroup for FILESTREAM, move (rebuild) the table on this filegroup.