Hi again!
After hours of testing I have come up with the answer to my previous question.

The following steps must be done in the mentioned order. I will explain how to upgrade XOOPS 1.3.x > 2.0.6 RC and at the same upgrade MyAlbum 1.0.x > 1.1.3. In the final step I will describe how you end up you having the superior MyAlbum-P module installed with all your previous photos in place.

1. Make a local backup of your xoops 1.3.x files and the db from your web-account!
2. Erase your entire content of xoops-files in your webaccount!
3. Upload a xoops 2.0.X release to your webaccount!
4. Upload the MyAlbum version 1.1.3. MyAlbum 1.1.3 (beta)
5. Now upload all your photos to the ../modules/myalbum/photos and ../thumbs.
6. CHMOD photos and thumbs catalogs to 777.
7. Install xoops again with another table prefix, i.e. 'test' (we do this in order to make sure that necessary catalogs have the correct privileges).
8. Now erase all tables containing the prefix 'test'
9. Upload, again, a fresh unused copy of the mainfile.php to your webaccount.
10. Run the installation again, but use your original prefix that you used for xoops 1.3.x
11. Follow and accept all upgrade questions!
12. Upload MyAlbum-P to your modules directory
13. Upload you photos from your backup to /uploads/photos and to thumbs.
14. Enter System/Modules and update the MyAlbum module.
15. Done!