What if my current H1B expired? Can I ask the new company to file the transfer application?
-If your current H-1b expires, your H-1 transfer may be or may not be fully approved (with I-94). You of course can ask your new employer to file a new H-1B petition for you no matter whether your current H-1b expires or not. You may provide the H-1B extension receipt when your new employer file the new H-1b applicaiton (this confirms your legal presence).
Does it make a big difference for the new company to file a new H1B application and file a transfer application?
-Only difference between these two is that you can work for the new employer after you file the H-1b transfer; but you can not work for the new employer until the new H-1b application is approved.
-If your current H-1b expires, your H-1 transfer may be or may not be fully approved (with I-94). You of course can ask your new employer to file a new H-1B petition for you no matter whether your current H-1b expires or not. You may provide the H-1B extension receipt when your new employer file the new H-1b applicaiton (this confirms your legal presence).
Does it make a big difference for the new company to file a new H1B application and file a transfer application?
-Only difference between these two is that you can work for the new employer after you file the H-1b transfer; but you can not work for the new employer until the new H-1b application is approved.