If it was grown from a rhizome it most likely spent all of it's energy last year making roots and some shoots for you and most likely didn't put any energy into making rhizomes. They usually begin forming after the crown is established so you probably don't have any to cut.
The easiest way to propagate is to take one of the shoots that's already popped up and gently bend it over and cover it with soil. Sometimes you get lucky and find one that's oriented horizontally which are much easier to get under the soil. After a few days or so, the growing tip will begin to pop out of the soil and you'll want to cover it up again. You can do this for as long as you wish but usually after a few weeks it should have developed a bunch of roots all along the stem starting from the crown outward. All you have to do now is to cut it away from the mother plant and donate to your friend. What you've basically done is create a rhizome. If you were to have left that portion covered with soil over the growing season it would have turned 'woody' and that growing tip would have grown you some hops. Easy as pie!
"Neil & I would've tweeted from the moon if we could have but I would prefer to tweet from Mars. Maybe by 2040" ~ @TheRealBuzz, Buzz Aldrin 11:20 PM - 04 Jan 13