You can configure your server to use the linux mail server to send email, but for the linux mail server to know to push received email to your system requires changes on it (normally in the aliases file -
certainuser:
certainuser@ourserver.ourdomain.com
As far as sending mail from your server to the linux server, you can put it's
name@domain.com into sendmail.cf. Look for the following lines (your lines may be a little different)
# who I send unqualified names to (null means deliver locally)
DRexchange.ourdomain.com
# who gets all local email traffic ($R has precedence for unqualified names)
DH
# class E: names that should be exposed as from this host, even if we masquerade
# class L: names that should be delivered locally, even if we have a relay
# class M: domains that should be converted to $M
# class N: domains that should not be converted to $M
CL unixtst
C{E}root
CMprivate.ourdomain.com
# who I masquerade as (null for no masquerading) (see also $=M)
DMourdomain.com
See
the Sendmail masquerade info and
Sendmail FAQ for more answers.