I have a quick question.

What kind of visa was he on?

As a quick tip, take a step back. Legally this is not your business - it's probably best for your girlfriend to speak with a local attorney who can guide her further. The last thing you want to happen is for Dad to assert that you're interfering with his relationship with his child. The court may also raise an eyebrow as to the timing here; the child has just turned 1, but you've been living with Mom for 6 months while she's still married?