Large language models are increasingly influencing human moral decisions, yet current approaches focus primarily on evaluating rather than actively steering their moral decisions. We formulate this as an out-of-distribution moral alignment problem, where LLM agents must learn to apply consistent moral reasoning frameworks to scenarios beyond their training distribution. We introduce Moral-Reason-QA, a novel dataset extending 680 human-annotated, high-ambiguity moral scenarios with framework-specific reasoning traces across utilitarian, deontological, and virtue ethics, enabling systematic evaluation of moral generalization in realistic decision contexts. Our learning approach employs Group Relative Policy Optimization with composite rewards that simultaneously optimize decision alignment and framework-specific reasoning processes to facilitate learning of the underlying moral frameworks. Experimental results demonstrate successful generalization to unseen moral scenarios, with softmax-normalized alignment scores improving by +0.757 for utilitarian and +0.450 for deontological frameworks when tested on out-of-distribution evaluation sets. The experiments also reveal training challenges and promising directions that inform future research. These findings establish that LLM agents can be systematically trained to internalize and apply specific moral frameworks to novel situations, providing a critical foundation for AI safety as language models become more integrated into human decision-making processes.