The spread of social misinformation has been a global concern, particularly affecting non-native speaker users who are more susceptible to misinformation on foreign social media platforms. In light of this, this study focuses on mitigating the challenges faced by social misinformation detectors in quickly regaining capability after crossing linguistic borders, especially for non-native users with only monolingual social media histories. By integrating sentiment analysis as an auxiliary, less sensitive task, we transform the challenging cross-lingual transfer into a manageable multi-task framework. Then, we propose HierMoE-Adpt, a novel, cost-effective parameter efficient finetuning method based on hierarchical mixture-of-experts adaptation, to enhance cross-lingual social misinformation detection. HierMoE-Adpt includes a hierarchical routing strategy and an expert-mask mechanism, effectively merge knowledge about the understanding posts in new language and misinformation detection capabilities, contributing to recover the performance of personal misinformation detectors in sync with the dynamics of personal international travel.