Prayer is the most important pillar of Islam after the Shahaadatayn. Not praying is major kufr that puts one beyond the pale of Islam. The evidence for this has been explained in the answer to question no. 5208.
It is not permissible for a Muslim woman to marry a man who does not pray, and it is not permissible for her to remain married to a man who stops praying after the marriage contract has been done.
As this man has recently become Muslim, it seems most likely that he does not know the rulings of Islam or the importance of prayer, or that not praying is kufr.
So it is essential to explain to him the status of prayer in Islam, and that not praying constitutes kufr, and that Islam and not praying cannot be combined. If he starts to pray then praise be to Allaah, but if he persists in not praying then he and his wife must be separated because he is not a Muslim.
It is very strange that your sister did not pay attention to this matter after you advised her. The relationship between them may not be proper according to sharee’ah, and we do not think that she would agree to that. You have to carry on advising her.
What we are afraid of is that your sister may not be praying either, which would make the matter more serious and more complicated.
With regard to working for or joining the American army, the ruling on that has been discussed in the answer to question no. 3885.
And Allaah knows best.