Whether your letter follows your inmate to a new facility depends entirely on which systems are involved in the transfer. Here is how it actually works.
If your inmate stays within the same system, the mail will get there. A federal inmate transferred from one federal facility to another, regardless of state, will eventually receive forwarded mail. The same applies to state systems. Mail sent to a state prison will follow an inmate to another state facility within the same department of corrections. It may take longer than usual, but it will arrive.
Where mail stops dead is at the boundary between systems. County jail to county jail is one of the most common problem transfers, and mail simply does not get forwarded between county facilities. Neither does mail sent to a county jail follow an inmate who gets picked up by the federal or state system. Those are entirely separate systems with no forwarding relationship.
If you sent a letter through InmateAid and your inmate transferred before it was delivered, contact InmateAid directly. For letters sent through the platform, InmateAid will resend to the correct facility at no charge. Just reach out and let them know what happened. It is a straightforward fix that costs you nothing.
The safest move when you know a transfer is coming is to hold off on sending until you have a confirmed new address. If the letter already went out, InmateAid has you covered.