See clip from Attorney Rajiv S. Khanna's conference call video that addresses this question.
This question has two sub sets, one is about an individual converting from H-1 to H-4 while they are processing their Green card and back to H-1 if necessary.
Second question which is also a FAQ, whether a Green card can or should be filed while somebody is on F-1 status.
For first part of question, wife is currently on H-1B, gentleman who posted this also on H-1B, I-140 is approved. Wife's employer is willing to start the Green card; wife is willing to move to H-4 EAD. So is that going to be interruptive of the Green card and the answer is No. The fact that she has moved from H-4 to H-4 EAD does not in any way interfere or interrupt her Green card process.
If PERM is filed, can she convert H-1to H-4?
She can convert H-1 to H-4 EAD anytime she wants. This has no effect on going process of Green card process and it is in my view reasonably safe. Of course there are pros and cons of both approaches, sometimes it makes more sense to stay on H-1 and sometimes it makes sense to go on H-4 EAD. Typically, I would say if you are I-140 is secured and your own status is secured, your job is pretty solid because remember her status is derivative of yours, if something goes wrong with your status it affects hers as well. Therefore, in my view its Ok to convert H-4 EAD if your job is pretty solid and your I-140 is not going anywhere. And if she wants to convert back to H-1 that too is not a problem, so going from H-1 to H-4 EAD and H-4 to H-1 is quite permissible and she will not be subject to the Quota, except when more than 6 years passed from her H-1 status.
So if she wants to convert back to H-1 within the 6 years of first approval, it is not a problem. She is not subject to the Quota.
Second part of the posted question was can we not apply for Green card while we are still on F-1 status?
First of all remember, filing for Green card is little deceptive, if you are filing for a PERM that's not really filing for Green card because in Immigration related forms the question asked is this, have you or has anybody in your behalf filed a Green card or an immigrant visa?
Immigrant visa is form I-140, so if you filed a PERM and PERM is under process that is not a Green card, technically. So is that Ok to F-1?
I believe so, I don't see any problem in doing that. The problem if any begin is when I-140 is filed, because a F-1, unlike a H-1, H-4 or L-1 or L-2 is not a dual intent visa, it requires you to have non-immigrant intent and by filing the Green card which is I-140 actually you are exhibiting immigrant intent that means you have traveled outside USA on student visa, your stamping of the student visa or even your school transfers etc. could be affected if at any time the question of your immigrant intent comes up. So if you travel out and CBP officer at the airport notes that you have a Green card going and if they find out they could decline your entry, and that is something to worry about, other than that filing a Green card on F-1 is not forbidden. In fact, like you noted sometimes, it may have been recommended because it saves your time.