Most police forces are strict in their interpretation of the word vermin, and it is unlikely to be the same as that applied by your landlords (Scottish Woodlands).

However, with your written permission to shoot deer on the land you lease, there should be no difficulty for your friend to apply for a variation on his certificate to include deer.

This assumes that he uses a rifle calibre that complies with Scottish law.

Failing this, he may well be committing an offence.