The tl;dr for the people not wanting to read through the court documents:
-guy lied about having a degree. Said he had two degrees and was finishing up his phd. Hr never went to college.
-Dude lied about being a Marine. Said he was in for 6 years and gave up a $250k job to serve his country and fight in Iraq. Actually, he enlisted briefly using a fake ID and got kicked out.
-lied about being in the Army. Said he served 25 years. In reality, he served less then one year and was kicked out when he told people he was gay.
-lied about income and being employed. Said he was a math professor at a college in TX. Was actually unemployed.
-lied under oath about $ he had declared when seeking restitution. Court not happy.
What Fox News fails to mention in their articles is the father made the claim of his wife scheming to transition his son at a custody hearing. He lost that custody hearing, in large part, because they found all the lies the father told. There is no evidence (and actually testimony against it) that the mother is actively seeking out medical treatment. It just seems like a hail-mary claim from the douchebag father as a reason to get sole custody of the kid.
This is just manufactured outrage.