Is it permissible to write a document stating marriage until a person can complete the legal contract in their home country, given the difficulty of official documentation in a non-Muslim country?

For a marriage to be valid, it requires the consent of both spouses, the woman's guardian (wali), and two upright Muslim witnesses. Additionally, both spouses must be free from any impediments. If these conditions are met and the contract is concluded with offer and acceptance, then the marriage is valid. Registration and documentation are for preserving rights and preventing disputes. There is no harm in delaying it as long as the contract has been concluded. It is desirable to announce the marriage to distinguish it from fornication, and it is preferable to promptly register it to preserve rights and ward off accusations.