bad times with authinfo, smtpmail, mu4e, davmail and mails providers

[Lazy Snail]

Hi,

I try to help somebody to setup its mails accounts with smtpmail.el,
mu4e, offlineimap, davmail, for gmail and outlook accounts, since
... nearly two months and countless readings over the internet...

For now with some up and down we were able to receive mails from all
accounts, but to send them throught only one account that is the most
simpler conf ;

I suspect that part of the problem is, let's say the we have the two
following mails address :

lisper@specific.do
lisper@domain.sp

1. they uses smtp.gmail.com as smtpmail-server, regardless of what say
their domain name.
2. they have the same username.

Does smtpmail.el and authinfo able to handle such situations ? If so,
how specify it to them ?

About davmail, in our setup the gateway is localhost. However I think I
have the same issue to specify it correctly in authinfo: how to specify
that localhost is only a gateway and that we want to authentificate with
eg, lisper@outlook.com ?

If smtpmail.el and authinfo fails to let us get it this way, what do you
recommend as smtp server ? postfix ?

plz help
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