Merging text messages backed up under two Apple IDs and iCloud accounts

I have historical text messages that were stored under one Apple ID (AID 1) for many years. On my iPhone, I logged out of AID 1 and logged in with a different Apple ID (AID 2). I began to use AID 2 and backed up my messages and other desired application files under AID 2, thinking that this backup would now incorporate the historical messages from AID 1 as well. I recently updated phones and attempted to pull my messages from AID 2 but only the messages from AID 2 are loading without the messages dating back to AID 1.

How can I merge the messages onto the same iPhone and back them up under the same Apple ID and iCloud account?