This has happened to me too, although I have been using a better email provider for some time, I haven't closed my old account. There are quite a few things to take into account when changing email providers.
Firstly, it is good practice to send out emails to large numbers of people by putting your own email address in the "To" field and then adding a blind copy - "BCC" field where you put in all the contact addresses. This means that all your recipients do not see the enail address of everyone else, just their own and yours.
However, you should be aware that if you try to send out large numbers of emails in this way, I think you may fall foul of the anti-spam rules and find that a temporary limit is imposed on you pretty quickly. You may end up having to send them out only a few at a time anyway.
I think you have until the end of May until fsnet is closed down. The letter advising you about this suggests you set up something similar to an "Out of Office" email where anyone contacting you on fsnet will get an automated reply. Your message could say that fsnet is closing and add your new email address. At least anyone contacting you before the end of May will be told of your new address. That may mean you don't have too many to contact when the servers are shut down.
If you have any fsnet emails that you must keep, make sure you have them saved on your PC or forward them to your new email address.
One other nuisance I've encountered is that your online identity is usually linked to your email address. Where you have to login to a website, you usually have to add your email address and password. All these accounts will need amending too. It's worse if you have set up your PC to "Remember login details". You will find it difficult to get access to these accounts if you don't change your email address before fsnet closes.
Fun isn't it! It's a pity email providers can't switch for you like banks and energy providers but then you'd have to pay for it! Best of luck.
