Ability Photopaint program offers users the possibility of export of their pictures (.apx files) to several other graphics formats, including JPEG format. You can do this simply by using the default File ► Save as.. function and select the JPEG format (.jpg, .jpeg) as output.
It is unlikely that any other software supports this type of .apx files, so using Ability Photopaint is most likely your only viable option for apx to jpeg conversion.