There is no service interval for the screen, and Suzuki does not recommend that it ever be cleaned in the service manual. I have personally put 135,000 miles on one Intruder, and 97,000 on another, without ever cleaning that screen, and on the one with 135,000 miles on it the screen was 95% clean when I took the motor apart. So while your advise is well intentioned, it is factually incorrect.
This screen is just a strainer that only blocks large chips and shavings from being ingested into the oil pump; the filter catches particles that are less than 1/100th the size of those caught by the screen. If your screen was blocked so much it stopped the oil from circulating then it is a symptom of a problem, not the cause of the problem. In order for the screen to be that blocked by sludge there was something wrong with the bike when you bought it, or the previous owner never changed the oil (and all the internal sludge broke free when you changed the oil), or the bike was abused by a previous owner beyond belief to shed that much clutch material. The motor died when the internal oil passages clogged, not from the screen, as it would be quite impossible for the screen, which is something like 4 inches by 3 inches, to get clogged up without the bearing oil passages, which are about 1/10th of an inch, getting clogged also. That's why you could not find a motor: when those little oil passages clog (or the bike is run out of oil), the bearing runs dry of oil, gets hot, and spins, eventually failing completely.
So keep the inside of your motor clean with lots of fresh oil of the correct type, and that strainer screen is irrelivant. But a visual inspection before you purchase a used bike, or every 50,000 miles or so, is a good idea: if the screen starts to sludge up, then the rest of the motor is already sludged up and the bearings are suspect.