Switch legacy email / domain server to Zoho Mail and on 13 Zoho One accounts

We have 13 Zoho One users but use a third party email and domain host / provider in Germany for the last 12 years. We experience synchronisation problemes with the German provider and sync with Zoho CRM and want resolve them. I think the easiest way is to switch to Zoho mail and make sure losing any of previous emails in the CRM system.