and I know the Halberstadt A.I called E.14,A.II called F.14 and B.1 called A.15,what was this designation series ?.
Those were internal designations applied by the Halberstädter Flugzeugwerke GmbH ... versus the official Idflieg designation applied for Luftstreitkräfte use.
There is conflicting information, however. According to
Kites, Birds & Stuff by P. D. Stemp (and airwar.ru), E14 was the internal designation for licensed DE
Stahltaubes used by the Halberstadt flying school (the Halberstadt
Taubes being requisitioned in 1914 as A I recce aircraft). But most sources say that E14 referred to the Idflieg's A II - a Halberstadt licensed Fokker M 8.
Most sources also say that Idflieg designation Halberstadt A I was applied to another version of the Fokker M 8. Oddly, this A I was a
follow on to Halberstadt's A II. K.W. Jonker listed "F.14" as Halberstadt's designation for the A II. If he was right, that leaves us with the A I/E14 puzzle. Was it a Halberstadt
Taube or a Halberstadt-built Fokker M 8? Or, less probably, was the Halberstadt A I designation repeated by Idflieg?
(Repetition seems improbable. Indeed, the Halberstadt B15 shows a reverse trend. That internal B15 was retained for two engine types which Idflieg distinguished between as the Halberstadt B II and B III.)
Another wrinkle is that the A I (M 8) may have
followed the A II (M 8). K.W. Jonker mentioned wooden-fuselage construction for the Halberstadt A II (vs Fokker's welded steel-tube structure). I wonder, is it possible that this A I was a follow-on because Halberstadt - despite its earlier
Stahltaube experience - was struggling with steel-tube techniques, and thus first adopted a more familiar wooden construction for their A II version?
The early Halberstadt-designed biplanes are less confusing:
Halberstadt A15 = Idflieg B I biplane, 80 hp Oberursel U.0 rotary
Halberstadt B15 = Idflieg Halberstadt B.II biplane, 105 hp Mercedes D I inline
Halberstadt B15 = Idflieg Halberstadt B.III biplane, 120 hp Mercedes D II inline
-- Internal B15 designation unchanged for higher-powered B III version
One presumes that Halberstädter Flugzeugwerke continued to apply internal designations to its designs but I haven't seen any corporate style designations mentioned in the context of their later aircraft types.