Can I replant this branch? Can it somehow be replanted in a pot?
From your pictures, it looks the leaves are from two different plants.
the top one is probably some species of lagerstromeria, maybe L. speciosa.....around here, they're called crepe myrtles.
the second pic is from something else, the leaves are completely different....maybe an albizia or acacia. Looks very much like an alibizia, except for the seed pods. If it is an albizia, it may be very difficult to propagate from cuttings