Other Issues: H1b Transfer After Grace Period Ended

Here is the quick background - Company A petitioned for an H1B in 2016, which was approved and became effective in October 2016 (and valid until August 2019). Unfortunately, I was laid off in July 2017, and have since been unemployed.

My question is - when I find employment with a new firm, am I able to simply transfer the H1B visa over to the new firm?

Other Issues: H1b Transfer After Grace Period Ended