Subitems are currently still in Beta which is why some functionalities, such as the ability to move subitems from one board to another, are not available yet.
Our developers are working hard on adding and enabling upcoming subitem features as soon as possible, so keep your eye out for this! In the meantime, you can keep up with the roadmap for subitems here. 
Please note that while this information is shared to outline some of our plans, these plans are subject to change.
I just had this same challenge in 2023 and wanted to share a couple of manual ways of doing this.
You can duplicate the whole pulse include subitems and move it to the other board.
I think that is a simpler way to aproach it. Why only move subitems?
Hi Franco, What do you mean by duplicating the whole pulse?
When I have tried creating an automation to ‘duplicate’ & ‘move to another board’ once subitem status changes to ‘done’ it duplicates on the board I move it to, not on the current board it is on. So essentially I create a copy only on the new board it has moved to. Is there another way to do this?
TIA for your insight & help!