How can I move received voicemail messages from one carrier to another?

I am in the process of switching my mobile phone service from AT&T on an old phone (Lollipop) to Google Fi on a newer phone (Nougat). I have a temporary phone number on the newer phone but once I get that phone and its equivalent apps fully functional I will have the old phone's number transferred to the newer phone thus ending the old phone's telephone and SMS/MMS functionality.

I have succeded in finding and installing all the equivalent apps though one of them is no longer available through Play Store but there are three voicemail messages on the AT&T server that I don't want to lose. I have shared them from Visual Voicemail to Textra and sent them plus their time stamps from the old phone to the newer one but I do not know how to get them from there to the Google Fi server so that the newer phone's telephone app can use its voicemail retrieval functionality to access them after I switch the phone number.

HOW can I accomplish this? Ideally I would like to restore not only the messages but also their time stamps.

Welcome to the AC forums.

You've done one better than I was able to a few years ago with an iPhone. In that situation I just ended up playing the messages and recording them to a recorder with an SD card through the line out of the phone to line in on the recorder to move them to a computer. Unfortunately, there really isn't a way to upload voicemails from a recording to your Fi voicemail unless you call your phone and play the recording to leave it as a message.

I was afraid that would be the case.

Will any voicemail that is received on the Fi before the number is switched still be accessible afterwards?

That would be a question for their awesome support team. When I signed up I ported my number straight over.

Calls on one number generally aren't available to another number, even if they're both yours. As hallux alluded to, record the VMs on the old number then, if you must have them available as VMs, call the new number and play them back. (Or just record them as .mp3 files and keep them on the new phone.)