The possibilities are endless when it comes to specifically pinpointing the possible stalker. However, I think it has to be one of three people. It could be the actual ghost of Jung Soo In, her close friend Lee Shi Jin (actress Lee Cho Hee), or former student Seo Young Eun. If it is Soo In's ghost, that would be very creepy and turn the whole series into a horror production. I know South Korea loves to release horror flicks in the summer too. I started to get scared when I found out the one sending messages to her actually died a year ago!
On the other hand, there are a couple of reasons I think Lee Shi Jin would want to terrorize Eun Byul.