Does an official divorce that the husband documented without the intention or aim of divorce, but rather to obtain residency in a foreign country, take effect, and is this considered a third divorce after the wife returned to him following the second divorce?

If the lawyer's authorization is to document a previous divorce and the husband does not intend thereby to create a new divorce, then a third divorce does not result from it. One must be cautious of marital disputes and strive to resolve them with wisdom, for divorce is not the first solution, and its origin is prohibition except out of necessity. Allah has encouraged reconciliation and reform.