Accurate and rapid state-of-health (SOH) monitoring plays an important role in indicating energy information for lithium-ion battery-powered portable mobile devices. To confront their variable working conditions, transfer learning (TL) emerges as a promising technique for leveraging knowledge from data-rich source working conditions, significantly reducing the training data required for SOH monitoring from target working conditions. However, traditional TL-based SOH monitoring is infeasible when applied in portable mobile devices since substantial computational resources are consumed during the TL stage and unexpectedly reduce the working endurance. To address these challenges, this paper proposes a lightweight TL-based SOH monitoring approach with constructive incremental transfer learning (CITL). First, taking advantage of the unlabeled data in the target domain, a semi-supervised TL mechanism is proposed to minimize the monitoring residual in a constructive way, through iteratively adding network nodes in the CITL. Second, the cross-domain learning ability of node parameters for CITL is comprehensively guaranteed through structural risk minimization, transfer mismatching minimization, and manifold consistency maximization. Moreover, the convergence analysis of the CITL is given, theoretically guaranteeing the efficacy of TL performance and network compactness. Finally, the proposed approach is verified through extensive experiments with a realistic autonomous air vehicles (AAV) battery dataset collected from dozens of flight missions. Specifically, the CITL outperforms SS-TCA, MMD-LSTM-DA, DDAN, BO-CNN-TL, and AS$^3$LSTM, in SOH estimation by 83.73%, 61.15%, 28.24%, 87.70%, and 57.34%, respectively, as evaluated using the index root mean square error.