Presheaf problem

Question

I need to show that the global element of a presheaf $P\in \widehat{\mathcal{O}(X)}$ is equivalent to global section of bundle of germs $\Lambda_P\xrightarrow{p}X$. In particular, I need help to show that if we suppose the existence of a global section of $\Lambda_P\xrightarrow{p}X$ then we can define a global element of presheaf. I was thinking that if $P(X)\ne \emptyset$ is easy then to show that exist a global element but i still don't prove that.