At the point of changing hosting service, you should change the domain name in order to find the new name of hosting. It is quite easy to do that; however, it does make a frustrating time, known as 'propagation'. It is the time in between the domain name change till the world see that change. Usually, it spans across the world from 24-72 hours.
When you switch email hosting you made a change at plenty of servers all across the world. A few servers request information change in 12 hours and some within in a few days.
You need to know that email system heavily relies on the reputation of IP address and send emails. There are a few ways of switching email hosting such as-
Prepare Plans of Leaving Email Hosting Provider
Use a malware removal service of WordPress to contact the owner of website for stop spamming and cleanup of the website. If hosting provider is not willing to do so, you can switch your email account within a few steps.
For this, you need to know the server's IP address that is currently used like IMAP or POP3 server. In addition, you also need the current IP address to send email. In most of the cases, it will SMTP server.
Then, search server's IP address from which you would like to receive mail. Post that, add an account to the email client via filling correct IP addresses for SMTP and POP3 server. New account need to be configured in order to ensure that messages put in the mailbox as in the earlier account. Now, it will be the default account.
Thereafter, you need to log in to the account where domain is recorded and then click space for altering domain point. Though, it might take time to broadcast for latest DNS information. While here, you can get emails from both of the email providers.
Also, you need to replace SMTP servers and IMAP/POP3 IP addresses with an ease to evoke names brought by latest e-mail provider. Then, cancel the earlier email account in client email in order to finish the process.