Hello bobfromswedesboro,
Thanks for the post in Apple Support Communities. I understand you have a question about file formats.
To clarify, you mentioned a Voice Memo and also voice recordings in the Messages app; was this recorded in the Voice Memos application and then shared? Or was it recorded directly from the Messages app and shared from there?
To clarify, is this a group message? Is everyone in the group using iPhone, or are some on other devices?
The .AMR format you mentioned is a compressed audio format. There's a setting that applies here, but it may be on the sender end; if Compressed is selected under Settings > Voice Memos > Audio Quality, it may explain why you're receiving a compressed file format. How is this set on your device? Are you able to reach out to the sender to see how it's set on theirs?
I hope this helps get you started.
Cheers.