Yes, she should block him, but she should also email him using work email saying:
Just to be clear, I'm not interested in you, nor am I interested in being friends with you. If you try to contact me one more time outside of work, I will report you to HR for harassment. Do you understand?
It's important to do this in writing, this way she has a time-stamped written record of her request with him. This answer is partially based on a previous answer I gave to a slightly similar question.
On a side-note, blocking him on Facebook/Instagram won't remove his existing likes on her posts/pictures, but it will prevent him from seeing her posts/pictures on his timeline from then on, so it will ultimately prevent him from adding future likes/comments on her stuff.