How to e-mail a check to someone

One way is to have the person sending you the check take pictures of the front and back of the check and then email them to you. Print the pictures out and use your bank's mobile app to deposit them.

If you need to physically walk into a bank with a paper check then there's no practical way to do what you're asking.

That being said there are much easier ways to do all of this these days, of course. Why would someone email you a check when they could use any number of apps to transfer it to you?