Movies Anywhere says to allow for up to 24 hours for titles to sync.
Movies Anywhere says to contact them through chat, email, or phone (weekdays 0600–2100 PT) for syncing issues or title-specific issues.
If you switched accounts on MA for any linked retailer account, then you can’t switch back for 180 days.
Obviously the linked title has to be natively available through all linked services. You can’t share to iTunes what is not available on iTunes at this time. Verify that (find the title on Apple devices).
Additionally, the Apple ID account has to be in good standing (not locked or disabled, no backlog on payments, valid payment method). Verify that (test-stream anything else from the Apple movie library).
Movie is missing from my connected digital retailer account - Movies Anywhere Help Center