You can't create another board directly on the Team-managed project. But you can vote for the feature request and follow it here: https://jira.atlassian.com/browse/JSWCLOUD-17371
In the meantime, you can create another board that uses a filter that includes a Team-managed project. You just can't use the project for the Location field of the board - you need to use your profile or another generic Company-managed project. But that won't affect the cards that show on the board.
Unfortunately, no, as per https://jira.atlassian.com/browse/JSWCLOUD-17371
You could create a board from a saved filter that was based on a Team Managed project, but the board would not behave the same nor look the same as the board originally created with the Team Managed project.
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