Illinois labor law?

I was fired from my job in Illinois with an international company, but I was rehireable after 30 days. I was rehired ASAP by the company, but I had a writeup in my file which they carried over to my new job, Can they do this?? Everything else, seniority, eligibility for benefits, was voided and started fresh like any new job.

The company is Walmart, BTW. I was a customer service manager and I handled a return that loss prevention later said was not our merchandise. HOWEVER--when I did the return, I checked the inventory system and the upc was in our system--so we carried the merchandise. The person also didn't get cash back--they got a shop card that had to be spent in our store. They also said that since i did the return, I should have had someone else do the override that needed to be done. I was told the night i was fired, that I could be rehired in 30 days. I only know what i was told--i don't know what's actually in the system. I would just like to have my original job back--i lost about 2 dollars an hour. I was fired as a CSM and rehired as a cashier--because they didn't have any CSM positions open at the time. I could have been rehired in my original position if there was an opening. I wasn't fired by the store manager--but he refused to reverse the decision.

If the information in the write up is accurate, yes they can put it in your file even though it was from a previous job.

The issue should be was the firing justifiable, since they were willing to rehire you.

Is it the same company? If so then yes they can keep your write up.