Transfer H1B petition filed as with consular notification

[simba123]

I'm working for company A for a little over a year now. I got my OPT extension and my employer filed H1B as consular notification. I got my approval notificaton - form I 797 B. If I have to switch jobs, can my new employer transfer this H1B or should I get it stamped before someone can transfer this H1B? If not, if they apply for a new H1B will I be considered within the cap limit?

Thanks in advance!