Is it permissible for the husband to take his wife back after the occurrence of a suspended divorce without her knowledge, and with her knowledge of the divorce? And what is the expiation for this divorce?

For a conditional or unconditional divorce to take effect, the wife's knowledge or consent is not required. The fatwa issued is that conditional divorce takes effect upon the fulfillment of the condition, whether the husband intended divorce, emphasis, or threat. Some scholars, like Ibn Taymiyyah, are of the view that swearing an oath of divorce with the intention of emphasis does not constitute a divorce but rather necessitates an expiation for breaking an oath. If a conditional divorce occurs and it is revocable, the husband has the right to take back his wife before her waiting period (iddah) expires, without requiring her knowledge or consent. It is recommended to have witnesses for the reconciliation.