Judy: denny had a surgery in Sharp Hospital on Friday, he can't work until Doctor diagnosis you may

1. Capital 'D' for Denny (it's a proper noun).
2. Surgery does not take an "a" - a person 'has surgery' or 'has an operation'. 
3. Change the comma for a full stop.
4. "Doctor" either needs the name of the doctor (if you are referring to a specific person) or else needs 'a' (if it can be any doctor) or 'the' (if it is a specific doctor but you do not know the name) or 'his' (meaning the doctor of Danny). Doctor is a common noun so only needs a lower case 'd', unless it is part of a title (eg 'Doctor Smith').
5. "Diagnosis" is a noun, and is the identification of the nature of a thing. The word you need is one that indicates the doctor giving permission to the patient, eg 'permit', 'declare', 'say'.
6. "You" refers to the person to whom you are speaking, in this case, Judy. To refer to Danny you should use 'he'.
7. All sentences should end in a full stop. 

So your note now should read: 

Judy: Denny had surgery in Sharp Hospital on Friday. He can't work until his doctor declares he may.