In your MASTER file, click on File, then Import Records, then File.
Find/browse your Updated fmp file/database.
In the 'Import Field Mapping' window, towards the bottom, select 'Update Matching Records in Found Set'.
match up the fields you want to update in the Master file by changing the symbol between them to an arrow --->
As you said the Phone number seems to be each records "unique id", set the symbol between the phone number fields to an Equals sign =
With the test i ran, the new/updated blank fields should overwrite/replace the populated fields in the Master db.