How to communicate with my girlfriend when my headmate flirts with her?

You have to get your headmate on board with your boundaries. If a headmate is pretending to be you there may be a very important reason why, but you also absolutely must find a way to cooperate with each other. Write stuff down in a place where you'll both want to look at it if your headmate responds. Make sure you have ways of communicating with your headmate and making sure you work out with them any boundaries you may have.