Its very important to understand, that unlike most Western philosophers, the Buddha's philosophy came as a side effect of his meditation and realization.

When you realize the non-dual nature of reality, that the split between subject and object is an illusion, your entire conception of reality changes radically. This realization, which is beyond concepts, allows the generation of ideas that are completely outside "normal" frames of thinking.

This present moment is not conceptual, it is real.

Actually it would be the reverse, since Buddha predates stoicism.

Though it is possible Buddha was partially influenced by pre-Socratic Greek thought and, in turn, later Greek philosophers were influenced by Buddhism (to put it in perspective, Socrates was roughly contemporaneous with Buddha).