Hack #1 a.k.a. The Poor Man's Single Sign On (SSO) - Part 2

Most of you will immediately think of setting / checking cookie values using the base domain name  (mysite.com in this example).  And, that is part of the solution.  However, there is not a server-side scripting language available on web-server b. 

You might say "but, can't we just ....[insert something to the effect of recreating the web-server b content / layout & etc. entirely and use language X to check the cookie values]?"  Technically we can.  But as is often the case, the answer from management is a resounding "no".  That would take too long and cause other problems challenges.

Earlier I hinted at using Apache's mod_rewrite to meet the requirements.  Today's hint is the following:
RewriteCond and RewriteRule

Things might seem obvious now.  But there's a twist coming.  And, it was relatively difficult to figure out.