2010 mailbox users cannot access 2013 shared mailbox. I tried with and without outlook anywhere. I am using separate name for each setup ex: mail2010.domain.com and mail2013.domain.com. On both setup, outlook anywhere configured with NTLM and external/internal had the same url.

Hi Add-MailboxPermission -Identity "share mailbox" -User test -AccessRights FullAccess -InheritanceType All Can you post any error about shared mailbox?Terence Yu TechNet Community Support

Is not an access right problem. I got this error: Exchange server not available.