Yes, that washer is called a thrust washer, and as "K" said, they have been on all OS engines for many years. Tower lists these at $1.89 discounted, but OS parts are high. You can get the thrust washer for the Tower 40, part number LXJB45 for 99 cents and Tower will ship it to you at no cost for shipping which they do for parts for Tower engines, only. And, since the LA and FP series use the same crankshaft diameter for .20-40 (.46 on the LA) engines, the Tower 40 part will fit on your FP.
The first LA engines had three bypasses as on the FP. They went to two bypasses on the 46 LA and on all later versions of the other sizes as well. Was it another cost saving measure, or was it, as OS says, because they got higher rpm from the engine without the boost port??? The boost port, the one opposite the exhaust, was added to the Schnurle design boost the high end rpm. I block it off to boost the low end torque at the expense of the high end rpm which we don't want or need. I don't think you can have it both ways unless you also then change the timing on the sleeve. So, and without measuring we can't tell, I do wonder if the timing has now been changed on these engines as well.
The early versions of the FP engines had fully machined from barstock crankshafts. And then they went to skipping a couple of the machining operations which certainly did NOT improve the quality of the engines. Then, with the LA series, they went to a cast crankshaft with only a couple of machining operations. They used this same crank on the last run of FP engines and it kept the FP number with the LA series. This is not an improvement. The liners on the first LA engines had extremely poor plating. This they have corrected with later models, but there were a few FP engines that used the same technique as well. I shipped a number of them back as unacceptable. One thing you may not have noticed is how thin the liner is on the LA. This has only one word of explaination: "COST". Brass costs more than aluminum. So they use more aluminum in the case which also has a word connected with it: "heavy". You should probably put washers behind the heads of the screws that hold the back plate on. Otherwise, these are going to dig in and the back plate will work itself loose. Then you will tighten it up and, with the head digging into the back plate, run out of threads in the case and strip the case. Not good.
Not good.