How to retain webmail accounts, including all emails, on changing service plan?

Hi all,

My hosting service plan shall expire in mid April, 2021Code:Shared hosting - WordPress websites
Unlimited storage space
Unlimited visits
etc.On renewal hosting plan, my hosting company will charge me normal fee, not that listed on their website. All plans listed on their websites are for new purchase. My solution to breakthrough is to buy a new service plan with another domain. I have 5 domains registered and hosted on their server. I did it 3 years ago and it works. The only problem is all my current webmails will lose as well as I have to do some minor work on moving my websites to the new hosting plan.

Code:My solution to lost of webmails
I advised all users download them to their PCs, such as Thunderbird Mail, an example.I'm looking for an alternative solution transferring all webmail accounts and their emails to the new service plan?

On Google searching I found;
How to Transfer Email Address to Another Provider (Step by Step)
https://www.codeinwp.com/blog/transf...ther-provider/

I wonder whether it'll work for me.

Advice would be appreciated.

Thanks and Regards