Previous approaches for foreign accent conversion (FAC) either need a reference utterance from a native speaker (L1) during synthesis, or are dedicated one-to-one systems that must be trained separately for each non-native (L2) speaker. To address both issues, we propose a new FAC system that can transform L2 speech directly from previously unseen speakers. The system consists of two independent modules: a translator and a synthesizer, which operate on bottleneck features derived from phonetic posteriorgrams. The translator is trained to map bottleneck features in L2 utterances into those from a parallel L1 utterance. The synthesizer is a many-to-many system that maps input bottleneck features into the corresponding Mel-spectrograms, conditioned on an embedding from the L2 speaker. During inference, both modules operate in sequence to take an unseen L2 utterance and generate a native-accented Mel-spectrogram. Perceptual experiments show that our system achieves a large reduction (67%) in non-native accentedness compared to a state-of-the-art reference-free system (28.9%) that builds a dedicated model for each L2 speaker. Moreover, 80% of the listeners rated the synthesized utterances to have the same voice identity as the L2 speaker.