Multiplexing and demultiplexing of optical orbital angular momentum (OAM) are critical operations in mode-division multiplexing communications. Traditional Dammann gratings, spiral phase planes, and optical geometric transformations are regarded as convenient methods for OAM mode (de)multiplexing. However, crosstalk between the different modes and the difficulty of mode multiplexing greatly limit their application to mode-division multiplexing communications. Here, using a set of inversely-designed phase planes, we demonstrate an OAM (de)multiplexer based on multiphase plane light conversion that can enable perfect OAM multiplexing communication. The sorted patterns are Gaussian-like and can be coupled easily into single-mode fiber arrays. Inputs from the fiber array are turned into coaxial OAM modes after the phase planes. OAM mode crosstalk generated by the multiplexer is less than $-20\mathrm{dB}$, with insertion loss of less than 2.6 dB. OAM modes are sorted by the demultiplexer with mode crosstalk below $-10\mathrm{dB}$, and the sorting results are coupled to the fiber array. OAM modes carrying 10 Gbit/s on–off keying signals were transmitted in a 5 km few-mode fiber. The measured bit-error-rate curves have power penalties of less than 10 dB. The proposed configuration is highly efficient and convenient and will be beneficial for potential applications in quantum information, information processing, and optical communications.