“Oscar Wilde wrote the novel, “The Picture of Dorian Gray.”
(Rewrite this sentence, using the noun from of the verb “wrote”.)
 Oscar Wilde was the writer of the novel, “The Picture of Dorian Gray”.
 Oscar Wilde is the writer of the novel, “The Picture of Dorian Gray”.
If  is right, please explain whether it’s ok to change the tense of the original sentence. If  is right, please explain why  isn’t correct.
Both your sentences are grammatically correct, but their meanings are slightly different.
The first sentence means that the writer is dead, but the writer is still alive in the second sentence.
The original sentence doesn’t imply whether the writer is alive or not.