I worked for a company and was let go I got unemployment and now the company is appealing it. How long can a company wait to file an Appel in sc?

I worked for a company in sc. Things were pretty bad at this place of business. I started looking for another job and I found one so I thought. I put in my 2 wk notice at the place I was working and on the Friday b4 the Monday that I was suppose to start the company called and said that they do not have enough work so they can not hire me. I went to my boss and explained to situation and asked if I could keep my job. I was told yeah not a problem. I worked the following week and on the following the director let me go. They said it was because they just did not feel like they could keep me on knowing that I was looking for another job. I filled my unemployment and got it. Now it has been 63 days later and I received a letter in the mail saying that the company is appealing my unemployment and I may have to repay everything that I have received. Is this legal and how long does a company have to file an Appel on unemployment in sc?