Adobe FrameMaker should be able to convert between its own BOOK and FBOOK formats simply with the use of File → Save as.. function.
Convert Adobe FrameMaker book file to Adobe FrameMaker Book file.
We have found one software suitable in our database for this conversion.
Microsoft Windows software - convert book to fbok on Windows
Authoring and publishing software from Adobe
Convert from book 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.