share data between server applications

What type of data needs to be shared? Data that is stored in a database or regular files?

You could open SQL port 3306 on server B so server A can access it directly (better to use ssh tunnel for encrypted connection).
You could sync all the databases (master-slave setup). If data on server A gets changed, that change is pushed to server B etc.
For files you could use rsync (over ssh) to keep files synchronised between two or more locations
You could write a php api on server B wich server A calls when it's need some data etc.