Non Cap extension - Upto how many years

Hi , I have got my H1B from my Previous company on 2013 . I received the approval notice on August 27 2013 , stating that its Valid from 10/01/2013 till 12/2/2015 .

I never used that visa and would like to know if I can still transfer the H1B visa to my present company with Non-Cap as its almost 6 years that I have received the approval notice.

If yes, then I would like to know what will be the last date that I can apply the renewal/transfer .
Thanks in advance .

This is slightly grey area…If you have not traveled to US and not got H1B stamped, then you may not be considered as counted towards cap, as you never had H1B status…

My H1B Visa was stamped but I never traveled with that and I am in US now with my L1A from my current company .

You maybe able to use the H1B and file as Cap Exempt as you had H1B stamped. I suggest you double check with your attorney and then file it as cap exempt…

Any idea until when I can apply for cap exempt ?

No particular limit as such…it used to be 6 years in the past, but changed with recent rules in 2017.