How to access Exchange shared mailbox from Thunderbird, different domains

I have an email address like [email protected] and I want to access a shared mailbox [email protected], where company1 and company2 are just different names at the same server.

I use Thunderbird/Postbox client instead of Outlook due to important religious matters. And everything works fine if the shared mailbox is @company1.com. I only need to set:

User Name: [email protected]@company1.com

However, working with company2.com like this:

User Name: [email protected]@company2.com

does not work at all - the password is not accepted.

How can I work with Exchange's shared mailboxes if the domain names do not match?

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