Is it permissible to establish an ongoing charity (Sadaqa Jariyah) with the intention that its reward be for the deceased if they were Muslim, and that it be a charity for those who manage it if they were not Muslim?

If a trustworthy person reports that someone embraced Islam before their death, then they are to be treated as Muslims. The absentee prayer (Salat al-Gha'ib) should be performed for them if direct prayer is not possible, and they should be buried in a Muslim cemetery. If their conversion to Islam is not confirmed, then it is permissible to supplicate for them and give charity on their behalf, provided they were indeed a Muslim, as the Prophet, peace and blessings be upon him, guided to making supplications conditional.