Spouce visa (h4) process while I'm on J-1 and my husband has H1B

[Vilma]

Hello,
I am on J-1 visa and my husband is H1B holder. My visa expires in December and I need to start applying for H4 visa. Currently we both stay and work in the US.
Can someone advice me on a couple of questions?:
My passport is under my maiden name, does my passport has be under husband's name?
Is it possible to get H4 while I'm on J1?
Which forms should I start to submit, having in mind I am currently in the US and holding J-1, which is valid till the end of December?
if I get H4 before my J-1 expires will I need to leave the country for stamping purposes?

Hope somebody has been in my situation before and can advice me on the action plan.
Thanks,

[shervin143]

My passport is under my maiden name, does my passport has be under husband's name?
>>> Not required.

Is it possible to get H4 while I'm on J1?
>>> Yes. A COS can be filed from J1 to H4. It has to be done before your J1 status expires.

Which forms should I start to submit, having in mind I am currently in the US and holding J-1, which is valid till the end of December?
>>> Form I-539.

http://www.uscis.gov/sites/default/files/files/form/i-539instr.pdf

http://www.uscis.gov/sites/default/files/USCIS/USCIS%20ELIS/elis-instructions.pdf

https://www.immihelp.com/sample-instructions-form-i539-extend-usa-visitors-visa/

if I get H4 before my J-1 expires will I need to leave the country for stamping purposes?
>>> Not required. Your COS if approved will come with a new I-94 attached. As long as the I-94 is valid, you can stay in the country as a dependent.

[Vilma]

Spouce visa (h4) process while I'm on J-1 and my husband has H1B

Can I submit I-539 form online? If not, which address should I post the form to?
Also, how long does it take to get the form approved?

Thank you,
Vilma

[shervin143]

Can I submit I-539 form online?
>>> Yes. But you still need to send the documents. Check the below link.

http://www.uscis.gov/sites/default/files/USCIS/USCIS%20ELIS/elis-instructions.pdf

If not, which address should I post the form to?
Check the below lins.

http://www.uscis.gov/sites/default/files/files/form/i-539instr.pdf

Also, how long does it take to get the form approved?
>>> 4-5 months.