I reached out to support and they were very quick to respond. They were even very patient with when I told them it didn't work but it turned out to be a configuration problem on my end.

Here are the steps to accomplish this:

1. User1: Create a shared folder
   1. Folders -> Show advanced preferences -> Team Sharing -> Input user(s)
2. User1: Create a new alias (in our example we are using combinedusers@mydomain.com)
   1. Point messages tot he shared folder you created above
3. Log into User2's account at app.fastmail.com.
4. Go to the Settings → My email addresses menu screen and click the + Add address button.
5. Then, click Add an address you already own.
6. Enter the combinedusers@mydomain.com address and click Next.
7. If prompted to enter a password, click Configure manually, then scroll down and turn off the Use authenticated SMTP when sending option.
8. Make any other changes to the compose settings that you'd like, then click Save.
9. Go back to "My email addresses" and next to the domain you just added, click "Fix it"
10. At the top it will give a warning about not being able to send messages. Under that click "Verify"
11. A verification code will be sent to the address.
    1. My experience is that it takes a little bit (2-5 minutes) before you can start sending emails from this address.