Is H1B Visa transfer possible although never travelled to US.

[John_]

I have H1B visa from company X till 2017. I have joined this company a couple of years back and got my visa stamped this January. I haven't travelled to US on H1B. Now I have resigned from company X and joined some other firm.
If my current company is willing to send me to US, am I eligible on that H1B visa or the whole process will start again. Starting from lottery and all.