Is it permissible for a scholar to be the guardian of a Muslim woman in a "Misyar" marriage, given that her father does not pray, and knowing that the husband does not intend to divorce and the marriage could become official after the mission ends?

Marriage without a wali (guardian) is invalid according to the majority of scholars. The persons most entitled to give a woman in marriage are: her father, then her paternal grandfather, then her son, then her full brother, then her half-brother (from the father's side), then their sons, then the paternal uncles. If the father loses the eligibility for guardianship, the guardianship transfers to the next in line. If she has no righteous guardian, then a Muslim judge marries her with her permission, based on the Prophet's (peace be upon him) saying: "So the ruler is the guardian of one who has no guardian." If it is difficult to find a Muslim judge, then a trustworthy and just man undertakes her marriage with her permission. Guardianship is not forfeited by fisq (transgression), and abandoning prayer out of negligence is considered fisq but not kufr (disbelief). The fundamental principle is to adhere to the conditions of the granting authority for the scholarship, as long as they do not contradict Islamic law.