What is the religious ruling on a man marrying when he claimed to have converted to Christianity to obtain asylum, while affirming his adherence to Islam, and is his marriage considered void in this case?

Anyone who utters a word of disbelief intentionally and willingly commits an act of disbelief thereby. The only exception to this is someone who is coerced, for they do not commit an act of disbelief. The threat of improving one's financial situation is not considered coercion.

If an apostate repents while his wife is still within her waiting period (iddah (definition)), he may return to her. However, if he repents after her waiting period has ended, it is more cautious to remarry her with a new marriage contract.