To do this you’ll need to create a new LUN on the SAN and present it to SQL_SVR_A. Then stop the SQL Server, move the database files to the new smaller drive, keeping all the folder paths the same. Switch the drive letters on the two volumes. Then start the SQL Server Service again. All your databases will now be available.
You can now reclaim the empty volume back on the SAN, delete the LUN, and extend the existing LUN on SQL_SVR_B onto the new empty space.
(This is the same answer that I posted here.)