West-German Paratrooper qualification badge 1956-1957 - Jump wings

[Jack59]

In this context. Could this be this badge?

Very possible, here is what wikipediia as to say:

When the Pentomic* concept that replaced regiments and battalions with battle groups was introduced in 1957, Companies A, B, and C of the 187th Airborne Infantry Regiment were redesignated as HHCs of the 1st, 2d, and 3d Airborne Battle Groups, 187th Infantry, respectively. The 1st ABG, 187th Infantry was assigned to the 11th Airborne Division in Germany from 1 March 1957 to 1 July 1958, when the 11th was inactivated and reflagged as the 24th Infantry Division. During its assignment to the 24th it was involved in the Lebanon intervention. On 8 February 1959 it was relieved from the 24th, rotated back to the United States and was assigned to the 82d Airborne Division at Fort Bragg, NC.

*Pentomic was a structure for infantry and airborne divisions adopted by the US Army between 1957 and 1963, in response to the potential use of tactical nuclear weapons, on future battlefields.

Have a look at this interesting link:
Airborne helmets with camo paint scheme or camo cover in 1958 - M-1; M-1C & M-2 HELMETS - U.S. Militaria Forum