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Hello, thanks for posting the code you are getting is specific to the a/f sensor, you're not getting a code for the converter which is a different code, the sensor can affect fuel mileage, stalling and low idle at stops is usually related to a sticking idle air control valve, it is located on the bottom of the throttle body, it can be removed and checked for sticking and can in most cases be cleaned using a carbon dissolving spray and a brush, while the throttle body is off it should also be cleaned. Are you getting both 1135 and 1155?
The P1135 code is for the a/f sensor bank one which is near the firewall the 1155 code is for the bank two which is at the front near the radiator, replace them both, use Denso brand sensors if possible, it's what Toyota uses.