I got a piano piece in which in multiple occasions, it seems it suggests me to play a note with right hand, and then use left hand to press the same key and switch to left hand. How should I play these? Should I switch hand (i.e. first press with right hand, then left hand on the same key, and then leaves right hand)? Or merge it into a longer note (i.e. press with right hand, and remains on the key. left hand will just omit this note)?
For example in the 2nd attached picture, can I just omit the B on the left hand?
Is this something with the transcription and it needs adjustments? if so, how?
I have seen other similar questions, but they were same note for same start and duration, so one can just play with one hand and omit the other. But here they start one after another, with a short overlap.