Børge Mogensen sideboard with a bent back: advice please  

Hmm.  One oddity is that the panel seems to have opposing grain direction on its two faces; if so, this is almost sure to induce warpage. Hard to believe it left the factory that way, but I guess it's possible.
The panel performs no structural function, I feel sure. It appears that it might have been designed  to be kept in place by the two horizontal battens on the rear.  If these could be replaced (as necessary) by broader ones, that should retain the back panel and keep it in shape. I wouldn't try to bend the panel to flatten it, as this would be frustrating and futile, I believe.
If the two vertical battens on the rear can be removed (they would have visible screws) that would make transportation much easier. I'd expect the piece to have been made that way . . .

Add another vertical board in the middle to straighten it. 
More pertinently, I am not convinced that the two pieces are unit. It looks like a marriage of two Mogensen for Søborg pieces. There are a number of things that make me think this:  the double Søborg stamps, the strange front posts that I've never seen on a Mogensen design before, and the odd construction of the this panel that has bent, which is very not like Søborg who were very good. Also the fact that the center panel is not the same type of substrate as the two cases is very suspicious (the center almost looks like Masonite from behind). 
I have some Søborg catalogs. I suspect I can find the two separate pieces.
But I also would not be surprised if you discover that there are little differences in the construction that prove the center is not original. Perhaps the screws are different?  The substrate is already known to be different.  Perhaps a wood is completely different than anything in the case pieces?  Perhaps the cuts look more crudely done?

That makes sense.  It would explain the battens -- those aren't typical construction for Danish case pieces, are they ?
It's not at all unusual for a layman to make a  panel like that and think that they could get away with veneering it on one face only.  Bowing as it has would be the expected outcome. Assuming it's only 1/4" thick, it will be easy to keep flat as Leif or I have suggested.

Checked the 1954 catalog. The center is a later addition. The bottom is model 160. The top is model 161.  In the catalog 161 sits directly on top of 160.  
If it were mine I would stack them as designed. 

I agree with Leif. Even if Soborg had decided to do something like this, and marry a two piece unit into a single piece, I do not think they would have done it in the way that it was done here.

Thank you all for your very informative and helpful responses. You have convinced me it is not original. I strongly suspected so myself, based on the crude grain and back construction, and this being the first time I see it. Also, those curved pilllars look like a slightly odd match for the style of the units themselves.
The board on the back of the panel is indeed masonite, and it is attached to horizontal battens as seen in the last photo, meaning the back will probably not bend easily, most certainly not without some sort of softening.
I will probably try to restore it to the original configuration. The battens should come off easily assuming they are only attached by those screws, but I am concerned that the pillars are glued in place. What do you think? If they are, how do I best remove them? 
The answer will influence the mode of transport. I would prefer disassembling the unit at the auction house, but this will not be possible if the pillars are glued. I realize this is just speculation, but there is not much else I can do before Monday.

I would expect them to be mounted with screws, unfortunately, as this will mean holes in the cases. 

You can cut the posts at the narrow point if you are sure you are going to reconfigure the unit as per the catalog. Then at home you can determine how the post is attached more comfortably. Even if their are holes, they will not be seen when the cases are stacked.

Thanks for your input. I am fine with screws; as glassartist notes, the holes will be hidden. Glue will be worse to deal with. Sawing the posts off at the middle is a good idea. I hope to find out tomorrow.

Inspection done. The posts are plugged, top and bottom.

Huh.  Someone really tried to make this look like original work ?
Perhaps, to preserve the neat appearance of those plugs, original or not, you might consider cutting the posts in half, and unscrewing them from their hidden fasteners (screws).  Then you'd have to cut off the screws at the surface.
Hmm.  Might not work; the screws would probably just turn with the posts.  So, you'll have to excavate the plugs, doing as little damage as possible, unscrew the posts, and re-plug the holes. I'd select a brad-point drill just a bit smaller than the plug, center carefully, and drill slowly until metal hits metal.

I figure this is a long shot, but you never know . . .
 
Last night, I picked up a Borge Mogensen #160 sideboard by Soborg. It's in very good condition, except for a missing internal sliding silverware drawer (flat shelf shown as replacement in top slot in the photo). 
 
By any chance, does someone out there have an extra Soborg flatware drawer for this sideboard style that they would be willing to sell? The sideboard is the 5' (150cm) version, so the drawer must be around 2'4" (70cm) wide.
 
I know it's a long shot, but when I posted a not-too-common Bruksbo Veggen wall unit here a couple of months ago, leif noted that he had a whole bunch of pieces from that design line in storage.
 
Thanks.

Perhaps you are not missing anything. I have had many Danish credenzas that had more mounting places than drawers. More than otherwise actually. It seems to be the drawer version of adjustable shelves. And that shelf would become useless in yours if you had another drawer. It is also my guess that it would have been possible to get a personalized assortment when originally purchased. Just my guessing though.

Does the shelf match the other pieces, or is it clearly a replacement?
It is entirely possible that Glassartist is right.  But I did a bit of digging, and the evidence would suggest that there are supposed to be 4 drawers, of flexible arrangement, and not necessarily felted or with silverware inserts. 
Evidence: 
Four Specimens:
http://www.lauritz.com/da/auktion/boerge-mogensen-for-soeborg-moebelfabr...
http://www.lauritz.com/da/auktion/boerge-mogensen-lav-skaenk-teak/i2973563/
http://www.lauritz.com/da/auktion/boerge-mogensen-skab-skaenk-af-teak-eg...
http://www.lauritz.com/da/auktion/boerge-mogensen-skaenk-af-teak-og-eg-m...
 
And another catalog photo: