Basically, Bahá'í Law pertaining to marriage requires that the parties intending to marry must obtain consent of all living natural parents. Further, the responsibility of the parents in giving their consent is unrestricted and unconditioned, but in discharging this duty they are responsible for their decision to God. Should the parents in their letter of consent, as you indicated, not name a specific future spouse, the House of Justice states that it could be accepted and it would be permissible to perform a Bahá'í marriage ceremony on the basis of such a letter.
- The Universal House of Justice (From a letter written on behalf of the Universal House of Justice to an individual believer, October 9, 1975; compilation: ‘Lights of Guidance’)