Shared Mailbox between 2 tenants

You cannot assign permissions to a shared mailbox to an account outside the tenant. One solution is to use Exchange's mailbox forwarding commands to make sure that any message sent to mailbox1 in tenant1 goes to mailbox2 in tenant2 as well (and vice versa).

You can use Set-Mailbox -ForwardingSmtpAddress to define a forwarding address in another tenant. And Set-Mailbox -DeliverToMailboxAndForward $True to make sure that a copy of any received message is kept in the target mailbox and forwarded to the mailbox in the other tenant.