Does Trello Board can be share accross organization?
There are multiple options to share a board. If you want to make it accessible to everyone then you can make it public. However, if you want to limit it to certain group, then make it workspace accessible (only workspace members will be able to see it then).
With Enterprise plan, you can restrict access to people within your organization https://trello.com/guide/create-project#create-a-board
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