Yes. In the board menu, Export gives you a .board.json for that board, or Export with linked a .boards.json that also carries the boards it opens, so the links keep working. In the other organisation, Import in the dashboards list, read the dry run (nothing is written yet), then Import.
What the file leaves out: the organisation, people, sharing, revision history and the definition of your own widgets. Those widgets move with the widget library’s own export.