@Tom C - The Move to account will only be available to the board owner. However, as a workaround, you should be able to use the Duplicate option from the three-dot/ellipsis menu and then whomever created the duplicate/copy will be the board owner and will have the Move to account option.

From your dashboard, the board owner can be seen here:
 

The person listed in that column for that board will have the Move to account option.