Exim e-mail forward

Exim e-mail forward

i'm with some problems, i think it's not too hard to solve, but i'm a
starter on this, it's really advanced to me, i'm a programmer, all i know
about servers is easy stuffs like configure web servers, my company is
facing IP block from Microsoft Hotmail, we are not able to send e-mails to
hotmail users from our IP, so we decided to rent a VPS somewhere to serve
as "relay mail server", so, when a user authenticate on our server instead
e-mail be sent by itself it will be sent remotly using our VPS. It's like
a forward but e-mail should have same headers, like from, reply-to, etc.
It should be the copy of the e-mail that would be sent by the main server,
but via our VPS. I'll try to draw it :P
.----------------------------------------------------.
| happy user sending e-mail using our e-mail server |
'----------------------------------------------------'
|
(authenticate)
|
.---------------------. .---------------------.
| our exim server | --(blocked)--| hotmail destination |
'---------------------' '---------------------'
|
(magic goes here)
.-----'
.-----------------. .---------------------.
| VPS with exim | ------ | hotmail destination |
'-----------------' '---------------------'
Hope you guys understand my problem, sorry if my english is bad, i'm
Brazilian :P
Thank you for your attention