Please understand that a parts house counter person is not a "service person". They sell parts, they are not auto technicians.
This the manufacture's answer to your question.
P0135 Heated Oxygen Sensor (Bank 1 Sensor 1) Heater Circuit Malfunction
•HO2S connector is damaged (check pins for damage, and for moisture)
•HO2S heater ground circuit is open or has high resistance
•HO2S heater Ignition circuit is open (test O2A fuse in fuse block)
•HO2S heater element has failed
•PCM has failed
DTC P0101, P0102, P0103, P0106, P0107, P0108, P0112, P0113, P0116, P0117, P0118, P0121, P022, P0123, P0131, P0132, P0134, P0137, P0138, P0140, P0151, P0152, P0154, P0157, P0158, P0160, P0200, P0300, P0401, P0404, P0405, P0440, P0442, P0446, P0452, P0453, P1120, P1125, P1220, P1221, P1258, P1404, P1441, P1514, P1515, P1516, P1517 and P1518 not set; engine running, ECT and IAT sensors less than 122ºF and within 14.5ºF at startup, HO2S signal from 425-475 mv right after startup, Intrusive and Scan Tool tests not enabled, MAF signal less than 25 g/sec, and the PCM detected the HO2S signal remained within 150 mv of startup HO2S signal for a predetermined amount of time based on the ECT and airflow inputs.
This code sets in 2 Trip(s).
This code will turn on the MIL (Malfunction Indicator Lamp)