Actually, the Friedrich in the winter camo were painted with a white washable paint over the standard RLM camouflage. And almost always , the Werk Nummer applied on the fin was overpainted with the white. So that's the reason it is not noticed usually. So it may be omitted, except the serial can be seen in a pic.
Whether the Gruppe emblem could have been washed up or not ... it could be just overpainted with the white like the Staffel badge. Then there wouldn't be any reason for removing of it. And it would be the easy way to do it, wouldn't it. IMHO the stain, where the inscription was applied, is the result just of cleaning the area with a thinner or just a water before applying.
But the size of the white patch on the engine cowling doesn't fit the 9 Staffel emblem size. See the pic with the "Yellow 3" and other kites of the 9 Staffel with the winter camo.
In my opinion the Bf 109F could be transfered from the another squadron of the III Group. The most possible unit is the 7 Staffel although the numbers and the group marking should be of the white. But I found a pic where it can be noticed that the squadron could use the yellow digits and group sign as well. The 7th Staffel early emblem was the winged clog and its location and size more correspond to the white patch on the engine cowling. BTW .. the equipment rotation among squadrons of the same group was something standard for the Luftwaffe at that time. Additionally the 7 Staffel was quartered on the same Siverskaya airfield, the 9 Staffel was in 1941/42.