Home directory does not belong to me - because of Knoppix?

[ml2]

I recently installed Musix (based on Knoppix, as I understand) and made a user called MyFirstName and made a separate partition for home directories. So there is a directory called /home/MyFirstName on that partition and it workes in Musix as my home directory.
Then I installed LinuxMint (Musix doesn't really work well, I only wanted it for one particular application - MuseScore. Which doesn't work well either, now that I think about it). Version Cassandra. It asked me during the installation, whether I wanted to import a user from a previously installed system, and I did choose to import the user MyFirstName from Knoppix. And in the next step of LinuxMint install, I made my username to be MyFirstName again. Which means that the home directory for me as LinuxMint user would be the same as for me as the Musix user.
When logging into Linuxmint as MyFirstName, I get the error message that my home directory does not belong to me and the system won't start.
If it is useful information - I can write on the same home directory partition from Windows.
What went wrong? Should I install LinuxMint again, and what should I do differently? Or can I fix the problem from Musix, by changing sth in the /etc/fstab or using some GUI?

[Husse]

Please write with a bit of space between sections - my old eyes have a problem with your text.
I must think about this

[Lolo Uila]

...If it is useful information - I can write on the same home directory partition from Windows.

How is that /home partition formatted?

[Husse]

Oh dear - it's not FAT or NTFS I hope
Then - well....