Refilling H1b after gap and working on H4 EAD

I had used 3 years of H1b few years back while working with employer A and then shifted to H4 and joined different employer B on H4EAD basis. So can I file H1B this year with employer B with whom I am working now without going through lottery?

Yes, you can. Read

Thanks that article is very useful, so can I start working with employer based on this H1 receipt or need to wait for approval?