The study investigates the acquisition of English copula be by adult L1 Arabic speakers learners of L2 English. It sets out to test two competing hypotheses with respect to the characterization of L2 acquisition in post-critical period non-native interlanguage (IL) namely, the Full Transfer Full Access Hypothesis (FTFAH)[1, 2] and the Failed Functional Features Hypothesis (FFFH)[3] which serves as the framework for the study. The FTFAH view holds that IL representations in postcritical period L2 acquisition can be native-like due to convergence on native-like representations. On the other hand, the FFFH claims that IL representations in post–critical period L2 acquisition diverge from the target grammar despite apparent native-like performance. There are altogether 240 adult L1 Arabic learners of L2 English subdivided into three proficiency levels. A grammaticality judgement task is designed to test the learners’ underlying knowledge of English copula be in past and non-past contexts. The findings indicate that although the adult L1 Arabic IL representations deviate from that of the native-like representations, the IL grammars are able to generate representations that account for the L2 data and that fall within the general constraints of UG.