On closer inspection, the bug was my own fault. There was an announced change how files need to be shared starting with Android 7.0 (Nougat), but I didn't realize to adjust file sharing in the Custom Maps 1.5 update.
For some reason map sharing worked on my tablet that runs Android 7.1.1. However, my phone runs Android 9 (Oreo) and I was able to reproduce the sharing problem on that. Luckily the fix was not too difficult, so I have already pushed a new version (1.5.1 beta 1) to beta channel.
Please install the new version and verify that map sharing works for you in the new version. If you are not a beta tester, you can join (and leave) beta tester group on web page
https://play.google.com/apps/testing/com.custommapsapp.android. Once I have heard some reports that the new map sharing fixes the issue, I will push it to all other users.
Thank you Laurent for reporting the bug.
Tim, about the sample areas around the tiepoints. If you are using Custom Maps 1.5, the sample areas are twice as large as before. What kind of device are you using? I can only imagine that you have a super high resolution screen that makes the sample areas look very small. Knowing your device manufacturer and model number would allow me to find information about your screen resolution and investigate the issue further. I feel that the current size of the samples is pretty good even if the map image is generated from PDF that is rendered at 300 dpi.