Our new friend Timmy wasn't with us for long.
We placed his cage near the patio doors which we left open. Suddenly, a bird outside started chirping and Timmy got very excited and started calling back. It was pretty obvious that his family was out looking for him.
So, we took his cage outside. Before too long an adult sparrow was flying around, landing close to the cage, then flying off again.
Here's a picture of them together:
I opened the cage door and, once Timmy had figured out how to get out of the cage, he flew off into the big fir tree where the sparrows often hang out.
Now we just hope that he can still perch OK with his gammy leg. But at least he's back with his friends and family.