We examine mode couplings in chiral fiber grating (CFG) with N-fold rotation symmetry in the cross section and show how the angular momentum matching condition in couplings determines the generation and conversion of orbital angular momentum (OAM) beams. Then we discuss interactions of OAM and spin angular momentum in single- and double-helix long-period CFGs excited by the fundamental core modes. Subsequently, taking right-handed elliptic-core long-period CFGs as example, we demonstrate a dual-OAM converter generating OAM beams with charge +2 and charge +4 at dual wavelengths, both with a conversion efficiency greater than 97%, as well as a broadband converter based on adiabatic coupling, with a bandwidth about 10 nm for a conversion efficiency greater than 95%.