Is a woman considered divorced if her husband deserted her and left her in a state of suspension for 15 years without a formal divorce or judicial khul‘, and is the marriage of the questioner to her valid in this case, and what should he do?

As long as you know that this woman was not divorced by her husband, and no شرعي judge ruled for divorce or annulment; then your marriage to her is invalid, and you must separate from her immediately. It is not permissible for you to remain with her after you have become aware of the continuation of her previous marital bond.

The woman must repent to Allah Almighty. If her husband has not divorced her or initiated khul' (divorce by mutual consent with compensation), then she remains his wife, no matter how long his absence. She has no way to marry anyone else unless she submits her case to the شرعي judiciary, so that they may rule for her divorce or annulment.

Know that a secret marriage is invalid by scholarly consensus if it is without a guardian and witnesses, and a secret marriage is akin to the marriage of prostitutes.

We also note that documenting divorce and marriage in courts involves great benefits, and neglecting it leads to tremendous harms.