You are right that they are not married according to the law of government.
But let me clarify my point. What I meant is that they are couple in the view of God. Just as Adam and Eve were a couple, although there was no government then to certify them. Marriage is something set up by God, and it's beyond any secular law. On the other hand, we of course also need to obey the law of government, as book of Romans teaches us. I would enourage lz and her boyfriend to get a certificate as soon as possible.