Large language models (LLMs) often reflect Western-centric biases, limiting their effectiveness in diverse cultural contexts. Although some work has explored cultural alignment, the potential for cross-cultural transfer, using alignment in one culture to improve performance in others, remains underexplored. This paper investigates cross-cultural transfer of commonsense reasoning in the Arab world, where linguistic and historical similarities coexist with local cultural differences. Using a culturally grounded commonsense reasoning dataset covering 13 Arab countries, we evaluate lightweight alignment methods such as in-context learning and demonstration-based reinforcement (DITTO), alongside baselines like supervised fine-tuning and direct preference optimization. Our results show that merely 12 culture-specific examples from one country can improve performance in others by 10\% on average, within multilingual models. In addition, we demonstrate that out-of-culture demonstrations from Indonesia and US contexts can match or surpass in-culture alignment for MCQ reasoning, highlighting cultural commonsense transferability beyond the Arab world. These findings demonstrate that efficient cross-cultural alignment is possible and offer a promising approach to adapt LLMs to low-resource cultural settings.