How do I create a link that when the user clicks, it will bring him to the Google page as shown below (with the To field completed):

Right now, what I’ve managed is to simply link him to https://mail.google.com/mail/#compose and this is what he will see:

Similarly, is there a way to achieve this on hotmail as well?
This shows the composition screen. To get the whole gmail interface, remove
&tf=1.If you also want to preset a subject, just add
&su=YourSubjectto the query string