We experimentally demonstrate efficient frequency doubling of a telecom 1560 nm distributed feedback diode laser with a 3 cm long MgO:PPLN waveguide with a conversion coefficient of 114%/W. We investigate optical inhomogeneities by measuring the quasi-phase-matching temperature curve. The ~2.7 mW of second-harmonic power at 780 nm is sufficient to detect the Rb D2 features using modulation transfer spectroscopy. The laser frequency is locked to a hyperfine transition of Rb D2 line and typical residual frequency fluctuation of ±86 kHz (rms) is achieved within 30 min. Our experimental scheme can be used for realizing robust, compact, and highly accurate Rb stabilized 1560 nm laser systems for fiber-optic communication applications.