When I use an organization email, how can I get the user's signature?

When I use an organization email, how can I get the user's signature?

Hello. I have the email of a CRM user added as an organization email.

Apparently, if an admin sends a mailing from that organization email, the signature that the user has in his settings doesn't get merged in the mailing.

Is there any way to get that signature merged? I don't want to hardcode it in the text since other users can send the same email template. And I don't want to ask the user to send the mailing himself since that creates a bottleneck.

Thanks!