You can import dBASE databases (.dbf) to Ability Database management software and export and save it as .adb file specific to that program. It looks this is the only way how to dbf to adb conversion as no 3rd party software is known to us that would support export to .adb files.
Convert dBASE III/IV database file to Ability Database database.
We found one software available in the database for this conversion.
Microsoft Windows software - convert dbf to adb on Windows
A powerful data management system Ability Office software suite
Convert from dbf 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.