No. The BMW cradle will only work with the BMW GPSRs. Although the BMW and the Garmin GPSRs are very similar, they are internally identified (via software) so that only the BMW one will take advantage of the four buttons on the cradle.
You can put a Garmin one into the cradle, it will fit, but you can't take advantage of the functionality that the buttons provide.
There is no fix or workaround for this. I can assure you that it's not something that could easily be worked around.
Michael