Urgent!!! On STEM forgot to inform my school about employer change

[s.shivi]

I am in a bad situation right now based on what i have read on the internet so far. I changed my job approx. 6 months back but forgot to inform my school. Now i need to submit my I20 with my latest(new) employer information for H1b application.
Is it safe now to inform my school about my employer change? will they terminate my F1 status? If they do so, how much would be my grace period?
Thank you for help