I have checked a big grammar book written by four scholars. It says: 1. Some verbs can take "as" or not take "as." It is optional. It is the decision of the writer. For example: a. His theories were considered (as) false. b. His theories were deemed (as) false. 2. Some verbs MUST take "as." For example: a. His theories were regarded as false. b. His theories were characterized as false. c. His theories were seen as false. 3. Another book says that verbs such as "consider" and "deem" should not take "as" because the idea of "as" is already in the verb. 4. That big book that I mentioned SEEMS to say that "declare" does not take "as." 5. I checked the "books" section of Google. I found MANY authors who wrote "declared false." I found only a FEW authors who wrote "declared as false." 6. Thus, I agree with you: probably it is better to choose answer A. Active: The government declared his theories (to be) false. Passive: His theories were declared (to be) false. P.S. That big book is A Comprehensive Grammar of the English Language. My 1985 edition has 1,779 pages. The authors are Quirk, Greenbaum, Leech, and Svartvik

please correct me if i'm wrong. I'm thinking both A and B are Ok ! for A, false can be regarded as an adjective/ for B , false is a noun.