I am reading Grillet's "Abstract Algebra" and I am confused about the application of the Universal property of the Module direct sum. The universal property is given by prop 3.2 in the book. 
One of the results of this proposition is the homomorphism between the direct sum.
I understand we can prove this result directly without using the universal property. But I wonder how does the universal property imply this result. Could anyone help me with this? Thank you very much!