Hi everyone.
An update. For me, thanks to Vasily, the problem is solved. 😀
Should anyone else be having problems migrating a Memento database with images (or any attached files) to a different Android device I list below the steps I took to successfully move my databases to a new device. Simple when you know.....
The first thing I should state is that you have to move all the Memento databases you have on the old device to the new one, you cannot just pick one or two from those on the original device.
The second point to note is that the process will overwrite any earlier copies of those databases that may be on the new device, even if they have been independently modified since creation.
And the third is that the resulting file that needs to be moved to the new device, can be large. Mine was 2 GB!
And so, to the process...
On the original device open Memento. Not just one of your databases but the "My Libraries" screen showing them all. Tap the 3 parallel bars at the top left, then choose the "Settings" cogwheel. Scroll down to the "Backup" section and select the cogwheel on the right of the "Backup" line. Ensure that the checkbox on the next screen is ticked and then select "OK". Now tap the "Backup" to the left of the cogwheel (not the "Backup" heading at the start of the section). You will then be asked where you want to save the resulting zip file. When happy with the location hit "Save".
Your next task is to move that zip file to the new device. Once you have done that open Memento on the new device, again at the "My Libraries" screen. As before tap the 3 parallel bars at the top left and then choose the "Settings" cogwheel. Again scroll down to the "Backup" section but this time select "Restore". You then need to choose "Select a backup file". From the next screen you need to select (See note below) the Memento zip file you just loaded onto the new device. Once you have selected the file you should get a screen warning you about any earlier libraries being overwritten. If you are happy to proceed select "YES" and wait for the process to finish. Then just enjoy your databases on the new device!
Note/warning: I had a problem at the point where I needed to select the zip file for restoring. The initial screen that was displayed did not seem to show the file so I chose my default file manager (Solid Explorer File Manager by NeatBytes) to find and select the file. The result was a screen that told me that the selected file was not a database. Very disappointing and annoying. However I have since discovered that had I been able to directly pick the zip file from the initial screen or use one of several other file managers, it works fine. So if you get a notification that the file you selected is not a database.... try a different file manager.
I hope that helps. If anyone has any questions on the above, please feel free to ask.
Hopefully you can all now freely move your databases as you wish.....
And once again, my thanks to Vasily for his help, and a really useful database.
WetMike