It's possible, but difficult. Like many other extraordinary feats like doubling your bench press in a month, it's most often seen in people just starting out.

In general, gaining strength means a caloric surplus, and in general, losing weight means a caloric deficit. There are programs like leangains that try to do both. There's a reason the "pros" have separate cutting & bulking phases, although that's maybe needless and arguably dangerous for mere mortals.

I suck at dieting, so I won't give specific advice other than perhaps troll r/fitness & co.