Thank you for your idea in regards to continuing development of the In Tray feature.
Currently you are only able to email the documents for the In Tray from an email address that has access to the a company file in the cloud. This is because it links the email address that you are using to the my.MYOB account which in turn links to the company file.
A workaround if you did have multiple email address that you wish to email from you would be to invite your other email address to the company file. For more information into inviting a user please Support Note: AccountRight - online user invitations
I would encourage other users that would like to see the ability to specific a non setup my.MYOB email address to email In Tray documents to to vote and comment if required.