Final Draft 13's and 12's collaboration system do allow all participants to edit the Beat Board (as well as script pages) in real time.
More information is in this video:
Older versions of Final Draft only allow script pages to be shared via collaboration.
Please note that all collaboration users must be on the same version of FD to collaborate. FD13 can only collaborate with FD13, FD12 only with FD12 and so on.
For information on upgrading to Final Draft 13, click HERE.
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https://fd.support/3WTY528