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The mathematical insights made by Paul Dirac were essential to his productive collaboration with Edwin Schrodinger, with whom they shared a Nobel prize in 1933, and to his own successful efforts to apply the special theory of relativity to the quantum mechanics of the electron.

A. to his productive collaboration with Edwin Schrodinger, with whom they shared a Nobel prize in 1933, and to
they refers to both D... and Ed...
it is illogical, as D only shared with Ed
A is out

B. to his productive collaboration with Edwin Schrodinger, with whom Dirac shared a Nobel prize in 1933, and to
to his ..., and to his ...
Parallelism is maintained, hold on to B

C. to his productive collaboration with Edwin Schrodinger, with whom both men shared a Nobel prize in 1933, and to
Same as A.
C is out

D. towards his productive collaboration with Edwin Schrodinger, with whom Dirac shared a Nobel prize in 1933, and to
towards his..., and to his...
Not a parallel structure
D is out

E. in his productive collaboration with Edwin Schrodinger, with whom Dirac shares a Nobel prize in 1933, and in
to+v shows motive. B can be preferred over E.
There is no as such grammatical mistake in E, just B is better.

B is answer.
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