|MLA Citation:||Bloomfield, Louis A. "Question 1549: Keeping an open soda bottle fresh"|
How Everything Works 21 Jan 2018. 21 Jan 2018 <http://howeverythingworks.org/print1.php?QNum=1549>.
By shrinking the volume of gas over the soda, your boyfriend reduces the number of CO2 molecules that must enter the gas phase in order to reestablish that equilibrium. BUT, when dense gas develops in the squeezed bottle, the high pressure of that gas will reinflate the bottle to its original size. The benefits of shrinking the gas volume will thus be lost.
To succeed in keeping more of the CO2 molecules in solution, you have to make sure that the squeezed bottle stays squeeze. That's hard to do. You're probably better off pouring the soda gently into a smaller bottle, one that just barely holds all of the liquid. That smaller bottle won't expand as a dense gas of CO2 forms above the liquid soda and the soda will reestablish its equilibrium without losing too many of its dissolved CO2 molecules.