SOLDIERX.COM Nobody Can Stop Information Insemination

Hi guys, i got a question for anyone who could have a clue or reference to the right solution

Say that Alice's computer has a certificate installed and bob's computer doesn't. Alice is able to access some web application since she has the certificate installed however bob can't.

If bob gained access to Alice's computer say via some exploit and he didn't want to hijack Alice's RDP inorder to access thoses application. Is there a known way that Bob can tunnel his web traffic through Alice's browser so that it can be authenticated with Alice's certificate inorder to access the same application?

Thanks