Import sound file into Music memos
Your music file must be a .caf file.
Open Settings → Music Memos and see what the ‘Use iCloud’ switch is set to.
You don't need to change it, just keep it in mind for step 5.
Find your music file in the Files app, such as in the Downloads folder if it came from Safari.
Long press the file and choose Move (or Copy).
If the switch in step 2 was on, find Music Memos under ‘iCloud Drive’.
If the switch was off, find Music Memos under ‘On This iPhone’.
Move/copy the file to that location.

This worked for me with a test caf file and iOS 13.5.