Getting it in writing, politely

Anything that matters should exist in an email. Not because institutions are dishonest, but because the person who told you on the phone will not be the person handling the case in April, and staff move.

A short message is enough: what you were told, who told you, when, and a request to confirm. Keep the replies in one folder with the offer letter and the receipts. If something goes wrong later, that folder is the entire difference between a conversation and a dispute.