I couldn't find an answer with the search

so hoping this is not a dupe question. Basically I'm moving from BS to BL and need to get new BL plates. However I'm not sure in which order I need to do things, do I go to the BS offices first to give back my current plates, or the BL one first to get the new plates?
Cheers
P.S moving appartment/cantons is a major PITA