SGH (SAS Ground Handling) lost LHG as a customer in 2019, way before SAS left *A. It is completely normal for alliance partners to have separate ground handlers, even in hubs. Landside, both AFKLM and LHG have been in terminal 2 for a while with SAS in terminal 3 (the terminal distinction does not make sense airside).
SGH was ordered to shed other customers -- only being allowed to handle SAS -- for a while as part of the reconstruction a few years back as a premise for receiving state support. I do not know how long this lasts, but I do not foresee them starting to handle AFKLM anytime soon.