Both .qbmb and .qbb files are used by QuickBooks software for some of their backup files, with the difference that the first file is used on Mac version and the second on Windows. Apparently, you can rename one to another when changing platforms. However, some users reported that they experienced fatal errors messages when they tried to import their Quickbooks Mac backups to Windows version. Your best option would be to to contact QuickBooks support.
Convert QuickBooks backup file to QuickBooks backup.
We found one software available in the database for this conversion.
Apple macOS / Mac OS X software - convert qbmb to qbb on OS X
An OS X version of popular accounting software
Convert from qbmb file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.