Every Delta(0)(2) degree is a strong degree of categoricity

A strong degree of categoricity is a Turing degree d such that there is a computable structure A that is d-computably categorical (there is a d-computable isomorphism between any two computable copies of A), and such that there exist two computable copies of A between which every isomorphism computes d. The question of whether every Delta(0)(2) degree is a strong degree of categoricity has been of interest since the first paper on this subject. We answer the question in the affirmative, by constructing an example.