Most smartphones have no problem connecting to your FastF hosted email accounts.
However, that means you have to set up your accounts correctly if you want to be able to access email from both your computer and your smartphone. If email is deleted off our server as soon as downloaded to your computer, it will no longer be accessible on your smartphone.
There is more than one way to do this, and most of them involve leaving email on your server at least temporarily.
The only caution on this is to not leave email on the server indefinitely. Email can accumulate on the server to a point where it exceeds the allowed limit and stops new email from coming in.
This is easily set in most email programs, such as Outlook, where you can specify to leave email on the server for a certain number of days after it is downloaded to your computer, then automatically delete it.