Hi Fuzzymo,
Thank You for your correct answer. It is clear! Such is life …
Just some comments:
1.: I have migrated my important stuff manually, because the Migration Assistant reported an incredibly statistic for me before starting.
2.: I have got a different proposal from Apple’s Help Desk yesterday for this issue: he advised to convert my old HD to an APFS format via making a disk image. It was failed during rewriting the disk, because changing the file system dos not supported by Disk Manager App. Anyway, I have tried the direct converting functionality of Disk Manager, but the product HD was not bootable even on my MacBookPro (2011) with High Sierra. After that I have posted my problem here.
3.: Anyway, I wanted to save my Mail stuff stored on my old HD. but I do not know, where is it stored on disk: I could not find this stuff by Finder App. That is why I wanted to boot from my old HD to Mojave. So, I have to forget this mails …
Thank You for your cooperation.
Best Regards
Dr. Józsa, László
from Hungary