My college is seperating from our parent University and I am attempting to setup the AD server for the following system.

Forest A is the parent university running Windows Server 2008R2

Forest B is our system running Windows Server 2012R2

What we want to accomplish is to setup a Forest Trust whereas any student from either school can log on to any computer under either forest.

With this Forest Trust, after we migrate user objects from Forest A to Forest B, will this maintain the sync of the users passwords between the two forests? The reason for this is that on Forest B we use Google Apps. for Education, Forest A does not. Forest A will not cooperate in running the Google Apps. Directory Sync or Password Sync.