It could just be that UNHCR has a unique leverage as a UN organisation - maybe they are seen as impartial or a benevolent international organisation. 

As a Muslim, I would suggest partnerships with existing Islamic charities such as Islamic Relief. You can leverage their brand as well as encourage them to explore more effective interventions in the longer term. I acknowledge there might be some pushback due to vested interests; however, I think it's worth a try  

FYI - I'm keen for this to work. I'm currently raising awareness to a Muslim audience on effective giving - happy to help however I possibly can.