by Ravi Alamuri.
Hello,
There are a number of ways you can achieve this. The easiest way I can think of, is using MNET. You can configure MNET to do bi-directional or unidirectional authentication (Only Moodle B users can access Moodle A, Moodle A users will not be able to access Moodle B). Essentially they will login to Moodle B, click on a link inside a block and be able to access Moodle A.
You could also use Database authentication or Web service based authentication or write a custom authentication plugin based on your requirements. We use a custom authentication plugin based on CAS to authenticate across all our Moodle sites.
Hope this helps.
Regards
Ravi