I have a map between string and a class object. I populate this map in Activity1 and i would like to pass it to activity2.
public class NEW extends Activity
You can encapsulate your data in a Bound Service as described in this document:
http://developer.android.com/guide/topics/fundamentals/bound-services.html
Don't forget to add your server to the manifest file.
this solution has the advantage of decoupling your data from your UI, which will ultimately lead to a more maintainable design.
If the need arrises you can add a messaging wrapper to your service's API to allow it to be called from other processes / applications