What you probably want is called a
CNAME Record. This is like a softlink to a domain.
You would add it wherever your DNS provider has the
A record you mention, and it would look something like
m.mainsite.example. CNAME m.example.org.
This tells the DNS resolver that whenever it sees
m.mainsite.example, it should go try and resolve
Note the trailing dots -- some DNS providers require them, some do not. When in doubt, use them.
Note that this doubles the initial lookup time for someone visiting your site; they have to do two lookups now.
A faster way that requires more maintenance is to just add an
A record for
m.mainsite.example that points to the IP address at
example.org. If you do that, you will need to update both in case of a new IP address, or a failover scenario.