What is the ruling on one who moved his lips, internally, divorcing his wife threefold without anyone hearing him, then did what he swore he would do?

The question contains three issues:

First: Conditional divorce (talaq mu'allaq) takes effect according to the majority of scholars, whether the intention was divorce or threat. This is the most preponderant opinion.

Second: Triple divorce pronounced in a single utterance counts as three according to the majority of scholars.

Third: If a person intends divorce in his heart but does not utter it, it does not take effect. However, if he utters it, it does take effect, and it is not a condition for others to hear it.

Based on this, this wife is considered irrevocably divorced from her husband with a major irrevocability (baynunah kubra). Therefore, it is not permissible for him to remarry her unless she marries another man, consummates the marriage with him, and then he separates from her.