Can I electronically trigger a PIR motion sensor?
People often use imprecise terms to describe InfraRed and it is further complicated in that with respect to Infrared "that word infrared ... I don't think it means what you think it means" in a lot of cases.
PIR - AKA Passive infrared sensors are pryoelectric devices that are optimized to detect Mammalian body temperatures (around 300 K), these warm bodies emit light at around the 10µm to 14µm wavelength range. Some people call this the "mid Infrared" but the trend is towards using the term "Thermal InfraRed" or TIR.
The IR LED you are using emits probably around 900 nm -> 750 nm - so close to 1µm in wavelength. Some people call this "Near IR" but those people also tend to call 2 - 4 um wavelngth range the "Mid Infrared also". Confusing? yep. It comes from a different historical use. One from the military one from chemistry/astronomy.
So you are at least a factor of 10X away in wavelength terms. And a LED emits light in a very, very narrow band of energies (it is an electronic effect after all)
Also PIR's are "designed" to detect rather largish bodies, which means a fair amount of energy or photon flux.
A black body emitter will increase energy in all wavelengths with increasing temperature. So an emitter at 27 C (300 K) will emit less light at 10µm than a emitter that is at 100 C (373 K) in the same band of energies. So if you want to have an emitter that will trigger the PIR, make a temperature controlled emitter, run it at 100 C to be safe, and it will emit a lot more light in the 10 - 14µm band than a body temperature device.
On second thought make it 70 C just to be safe. 100 C is a little too hot. Read up about blackbody emitters for fun.
You may be able to cause it to trigger if you place two filament bulbs operated under-voltage at a dim glow in front of it, you may have to tune the positioning a bit to get it right. Then switch them on alternately hoping that they will illuminate the alternate parts of the sensor. The spacing of the bulbs should be related to the detection 'beam' angle which can be different in different directions and zones and obviously will vary by model and manufacturer as well. The alternating frequency will need to be made to match the expected signal it would get if a person was crossing the detection 'beams' and getting it to match walking speed.
EDIT:
A domestic PIR sensor is designed to detect moving IR sources. They generally have a two active area detectors that have to have the areas alternately illuminated to create an alternating differential (pyroelectrically generated voltage) so they can detect a warm body moving but not a stationary heater. The alternating signal is normally achieved with the multi-zone Fresnel lens (or reflector) found on this type of sensor. To spoof it you need to place two sources that illuminate the two zones unevenly and then alternate their signal to mimic the flickering pattern that a moving person would create. A single source may not cause the proper alternating signal to be generated and be filtered out as spurious environmental changes.
A small quantity of warm but not boiling water will often trigger a PIR (safety in mind) or on a cold day just tap water - just throw it into the air near the sensor. Alternatively a few drops of cold water from a fridge or well will trigger on a warm day. Alternatively a well trained cat can help.