We are moving 2 websites to hostpoint.

We just moved the first domain.
Domain name by registrar infomaniak.ch
Old provider green.ch
New provider hostpoint.ch

Now, the problem is that, apparently, it takes much longer for the servers to change the MX-records than the DNS records.

Any advise how to better synchronize the 2 parts of the transfer (MX (email servers) and DNS (web servers)?

My idea would be to change the MX-Records first and once it is done, then change the DNS records.

I am not sure though where to request the change of the MX-Records?
By the domain name registrar (Infomaniak)?
Or by the old web provider (green.ch)?

Thank you for your inputs.

Normally your new hosting company will help with the transfer an guide you through the steps, as long as you approve all the transfer requests online and promptly the whole process can be done in 2-3 hours.

Well, they did ... Except they didn't mention that the mail servers transfer will take up to 3 days to be completed!!!!