This is an interesting discussion.
Moving to the new team, I still have my old responsibilities coming with me. Maybe later they will not add new tasks to me, but so far I still own those projects and deal with issues and requests day by day. With that, taking another person's full load to my shoulder, and I have to teach myself a whole new tool from scratch... so, I'm fine if he wants to take over some of the work, but that's not his excuse to dump his own work to me.