If you would like to authorize someone to pick up an x-ray on your behalf, here is a sample authorization letter for an x-ray.
To, [Name of concerned doctor]
Dear, [Name of concerned doctor]
I, [Your name] hereby authorize my sister [Your sister’s name] to collect my X-Ray of [Body part] taken on [Date] from your clinic. This X-Ray is for the purpose of [State the purpose] and it will provide a more accurate diagnosis.
My sister will collect them on [Date] with sufficient identification proof to avoid confusion. Any inconvenience caused by this is regretted however, it is not possible for me to visit your clinic today as [Reason].
Thanking you for your cooperation.