You actually cannot "convert" .rem files from Blackberry phones back to original .jpg files with some kind of converter. You have to disable the encryption on your BlackBerry device in order to remove the REM extension and get your original JPG picture back. For this you will need to use the BlackBerry desktop software as well as known the encryption key.
Convert BlackBerry encrypted data file to JPEG bitmap image format.
We found one software available in the database for this conversion.
Articles and other information relating to rem into jpg conversion:
How to disable REM media file encryption on BlackBerry - Disabling the media file encryption on BB devices
Microsoft Windows software - convert rem to jpg on Windows
RIM application used to synchronize of BlackBerry smart phones with PCs
Convert from rem 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.