I'm reading the book "*Elements of the representation theory of associative algebras, volume 1*". And I can't understand the proof of the proposition 3.11 on page 124 (the place where marked green).


[![enter image description here][1]][1]


"because $P$ is injective, $u$ factors through $P$". How to get this result?


  [1]: https://i.sstatic.net/tl0Tf.png