taken on someone else's role
Sheila is the Inspector's proxy because she takes on the Inspector's role of being a didactic vehicle to teach and spread the importance of having a collective social conscience
this is shown when Sheila emulates the Inspectors words during his final speech - Sheila states "what he made me feel , fire and blood and anguish", The Inspector states "fire and blood and anguish"
Reason she is the proxy of the Inspector - Sheila is trying to carry the message of socialism and enlighten her ignorant family about the hellish and eternal consequences of capitalism