Can a girl get a breast reduction from 34H to a 34B, or even better to a 34A? Scars will be similar?

The enormous breast reduction will require maintaining blood supply to the flap. The thickness of the flaps are the limitations mag factor on size reduction. An experienced Board Certified plastic surgeon will guide you.

Thank you for the question. 
 It is possible to reduce the breasts size very significantly. The concern with the amount of tissue removed is related to blood flow to the remaining tissue; if too much tissue is removed in one operation the blood flow to the remaining tissue (including nipple/areola) may be compromised. Part of the tissue that is left in place is called the “pedicle"; this segment of tissue is responsible for delivering the blood supply to the nipple/areola tissue. If the pedicle is made too small (in the effort to reduce the breasts as much as possible) then patient will likely have problems with tissue survival.  
For most patients in your situation, we have been able to decrease the breast size very significantly and achieve the patient's desired outcome with one operation.  Sometimes, a two-stage approach will allow for safe reduction and achievement of the patients' "very small" desired outcome.  Much of course depends on the patient's starting anatomy and carefully communicated goals.
My best suggestion: seek consultation with board-certified plastic surgeons who can demonstrate significant experience achieving the types of outcomes you will be pleased with. This careful selection of plastic surgeon will be the most important decision you make.
Before undergoing the breast reduction procedure it will be very important to communicate your size goals with your surgeon. Most patients wish to achieve a enough of a reduction to help with their symptoms while remaining proportionate with the remainder of their torso. I suggest that you do not communicate your goals in terms of achieving a specific cup size. For example, a “A cup” may mean different things to different people and therefore may be a source of miscommunication. In my practice, I ask patients to communicate their goals with the help of goal photographs.
I hope this, and the attached link/video, helps. Best wishes.

It is very difficult to give you much advice unless you are examined.  Photos will help us out online, but again it still would be a guess.In general, if you are a true H cup, I would say it would not be possible to reduce you enough to get you to a B or an A cup.  The reason is that some breast tissue needs to be left behind so that the nipple and areola could nourish and live off of.  Without the adequate amount of breast tissue left behind you would loose your nipple and areola.Certainly a very small breast size can be obtained but it really depends on what you are starting with.  Visit with a board certified plastic surgeon and get some opinions.Good luck.