(A) however he may choose to do so
Correct(B) in order to choose to do so
Illogical meaning; this literally says that CEO have to abide by relevant state tax laws in order to choose to report the earnings. One should remove "choose" to have a meaningful sentence
(C) in whatever ways he is choosing to do this
what does "this" refer to? wisdom suggests that "this" refers to "reporting the earnings...". This would give us "to do reporting the earnings..." it is awkward, just say "to report". Also "it" would be better than "this"
(D) by choosing to do this
Same "this" error. Also this sentence illogically suggest that because CEO's choice of reporting, CEO has comply with the laws. As if he was somehow didn't need to abide laws before
(E) when he chooses to do so
"when" suggests an illogical meaning. It literally says that CEO abides law only when he reports as if he is somehow above the laws when he doesn't report