Maybe I'm getting tired of saying it, or maybe it just needs to be done... But I'm gonna say it right here, right now:
There is an unfixable bug in the branch mission aka the recruitment mission. This bug prevents the second email from sending if you choose to hack into the attached PC. However, there is a workaround.

Simply save, exit the extension, then go back into it. From there, you should receive an email.
Have fun, and enjoy getting the good ending!