moving away from zoho

moving away from zoho

Hi

Can anybody confirm the following for me.

I want to change my MX records so that my personal domain name email no longer goes to ZOHO but to another.  If I do this, my understanding is 

1. All new emails go to the new webmail account provider.

2.  All my old emails still be available to read via ZOHO for as long as my contract lasts?

Thanks

Drew