DBCC Shrinkfile after full backup restoration but before differential restoration
Please advise if i can run the command DBCC SHRINKFILE with
  TRUNCATEONLY between full backup restored and before differential
  backup restoration.


No, you cannot.

You'll get the error that your database is in the middle of restore, and this is logic, you cannot do anything with database that is restoring.

You should analyse your db free space using sp_spaceused to understand if you can and should do anything with this database BEFORE you take the last backup, may be your db is in the full recovery model and log backups are not made regularly?