Vivek:
I am doing the same thing as you, but I am a few days farther into the process. After you send the form in, you can check the transfer status online. I think it is at this link, after you log in;
https://scs.fidelity.com/customeronly/s-statustoa.shtml
It will show a file number, initiation date, and estimated completion date.
My case shows an initiation date of July 2 and an estimated completion date of July 21.
Oakmark does not use "ACAT", which is some type of high-tech transfer method that would speed the process, so I assume it is all done by US mail, which slows things down a bit.
I think the info earlier in this thread about how to fill out the form is correct. I talked to Fido about whether or not to mention State Street--he said it probably did not make any difference, so I did not mention them and just stuck with "The Oakmark Funds", and it seems to have worked OK.