Capture One sessions between Mac and PC

Here's the pickle: the images are being sorted in Capture One [flagged, rated, colored]. That is being done on a Mac [Capture One 6].

Now comes the issue - when that session is being opened on a PC, the error pops out:

"Session file is of an incompatible format possible originating from a mac version of capture one"
- on a computer with Capture One 6 [which is ok, I suppose /6.4]

and

prompt to repair the database, but then giving an error "Database check failed"
- on a computer with Capture One 7

Is there any workaround. Even ant Google does not show up.

I asked this question at Phase One's support and got the following response:
sessions as well as your software key is interchangable between platforms.

I would suggest you follow up with them as it is not working for you when they say it should be.

About what version you asked? 6.x to 6.x does not work. I cannot see marked pics on import to 7th as well. Only after ACTUAL importing there is possible to see marked images [But I do not feel, that I should be happy about it, because it, emmmm, a big pain in the workflow. I am on recieving end and the coworker, who is working on Mac with 6.x software, says, that he does not have an option of "export to selects", that I see in my 7th version. Where's the truth?

p.s. because that "export" option would be, still efffed up, but still, a workaround.