Using Mail-in-a-Box mail server as a relay

Dear all !! ,

I have a small problem that i hope this software package will help me solve.

So I have a printer that can send emails. but is quite stubborn with getting the login into our typical emails (like office 365, Hotmail , gmail , outlook and so forth)
so I presumed i could create a mail server to get the email form the machine ( that i can monitor and see what is going wrong in the configuration of both the machine any the server.
and then use the server to send the emails it gets from the printer to a legitimate email with the email used in the previews email ( the one was send from the machine)

as a small representation.:
(MFP,Printer is se up to use an email that the mail-in-a-box has) send Email to :test@hotmail.com —> Mail-in-a-box server (gets the email) then forwards it to ---->test@hotmail.com via an email address (printer@hotmail.com) ----> the Recipient< test@hotmail.com> sees that the email originated from printer@hotmail.com

this is all i need it to do. yes it would be better to make my own email. But I have a residential line at home. And i know if you manage to get black listed you are more or less done. and I don’t want to bother with host names , and DNS , and all of that. I just need an intermediate guy to send the email from that machine because it just can’t or does not like the settings from (gmail,hotmail,outlook)

I would be grateful for your input
Thank you in advance

Simpler and more cost effective solution is to use Postfix on a fresh ubuntu 16/17 install:
(Instructions say debian, but ubuntu has the same package names and configuration files as Debian)