Precision measurements of transverse momentum-differential elliptic flow, $v_2(p_{\rm T})$, of identified particles have been done in p + Pb collisions. The characteristic mass ordering of $v_2(p_{\rm T})$ at low $p_{\rm T}$ and the grouping/splitting of $v_2(p_{\rm T})$ for mesons and baryons at intermediate $p_{\rm T}$, which have been regarded as the smoking gun of QGP signal, are observed in p + Pb collisions. However, the exact physics mechanism is not entirely clear. A multi-phase transport (AMPT) model incorporating a partonic phase followed by quark coalescence mechanism can reproduce the flow measurements. The mass ordering can be reproduced in p + Pb collisions by the default AMPT, while the grouping/splitting remains challenging. This work improves the coalescence in AMPT model by implementing an accurate quark phase-space distribution, which reproduces the measured grouping/splitting of $v_2(p_{\rm T})$ at intermediate $p_{\rm T}$ in 0-20$\%$ central p + Pb collisions.