Probably if the cost includes materials, his work looks good, and the labor is warrantied for at least a year. I'd probably opt to try to change out the wood on that frame in general though. You might want to see what your dealing with behind that wood, as it already looks like repairs have been attempted, and you want to make sure that this stops any issues back there more than superficially. If you go with the initial plan, make sure that the materials being used are of stronger quality/longer lifetime and rated for outdoor application. Get the warranty in writing somewhere if its not included on the invoice.