Answer
The charge on the outer surface of the shell is $-5~\mu C$
Work Step by Step
There is no electric field inside a conductor. Therefore, the inner surface of the shell must have a charge equal in magnitude and opposite in sign to the charge on the sphere. The inner surface of the shell has a charge of $+6~\mu C$
Since the total charge of the shell is $+1~\mu C$, the charge on the outer surface of the shell is $-5~\mu C$.
