When a letter feels too slow, you have a few options worth trying.
The fastest is to call the facility directly and ask nicely. This works about half the time and depends entirely on who picks up the phone and how the conversation goes. Be polite, be brief, and be straightforward about what you need. Something simple like explaining that your number changed and you just need someone to pass it along to your fiancé goes further than a complicated story. Staff are more likely to help when the request is easy and the person asking is respectful. It is technically bending the rules on their end, so the tone of the ask matters.
If your fiancé has already called and reached a voicemail or a disconnected message on the old number, that silence on his end is already telling him something changed. Getting the new number to him through the facility cuts that uncertainty short.
A letter through InmateAid remains the most reliable backup if the phone call does not work out. It will reach him in about a week and costs less than a dollar. Send it the same day you try calling so both options are in motion at once.
If there is anyone else on his approved contact list who still has the old number and can relay the new one, that is another bridge worth using until he has it directly from you.