Why did Han Solo change his mind in the end of New Hope?

Question

Is there any in-movie explanation in A New How explaining why did Han Solo change his mind?

We see him packing the cash that he received for saving Leia, and some moments / hours / time later he is saving Luke Skywalker’s life and, eventually, the whole Rebelion. A (too) important change to be made in such a quick period of time?

I am aware of this great answer, but my question isn't a duplicate (at least in my opinion), because that answer is by far more general (on getting Solo from Imperial to Rebelion side) and — what is the most important for me — it is based on many additional sources in the Star Wars franchise.

Here, I am specifically asking, if it is explained for sole A New Hope watcher (and I somehow missed it), why Han Solo changed his mind / side / attitude so rapidly? Or if in the context of this movie only the simple answer is "no, it wasn't clearly explained"?

Answer 1

No. There's nothing in the film/s that specifically indicate why Han came back other than the exchange that occurs shortly after.

LUKE: I knew you'd come back! I just knew it!

HAN: Well, I wasn't gonna let you get all the credit and take all the reward.

Luke and Han look at one another, as Solo playfully shoves at Luke's face. Leia moves in between them.

LEIA: (laughing): Hey, I knew there was more to you than money.

We're just left to assume that he changed his mind after having left his friend to fight the Death Star on his own, possibly with the encouragement of Chewbacca who we now know was a decorated war hero and long-time supporter of the Jedi.

---

For a better explanation we need to turn to other sources. The new Junior Novelisation adds a little bit of additional speech.

Han shrugged. “Well, I wasn’t gonna let you have all the credit!”
Chewbacca growled behind Han, giving the captain a little shake.
“All right, all right, and because we wanted to make sure you got out of this mess in one piece!” Han said. “How does it feel to be a hero?”

_{^{A New Hope: The Princess, the Scoundrel, and the Farm Boy}}

As does the original trilogy novelisation written by Alan Dean Foster George Lucas

“I knew you’d come back,” Luke was shouting, “I just knew it! I would’ve been nothing but dust if you hadn’t sailed in like that, Han!”

Solo had lost none of his smug self-assurance. “Well, I couldn’t very well let a flying farm boy go up against that station all by himself. Besides, I was beginning to realize what could happen, and I felt terrible about it, Luke—leaving you to maybe take all the credit and get all the reward.”

_{^{Star Wars: Official Novelisation}}

The official databank article on Wookiees gives us this snippet

Chewie helped convince Han to intervene at the Battle of Yavin

And in a novel set shortly after the Death Star's destruction, Chewie and Han have a brief discussion about his reasons for returning. Han confirms that his primary reason for coming back was his desire to help Luke. Chewie seems to be of the opinion that it was also about his desire for a financial reward.

“Name one time. Name one.”
The Wookiee rumbled and began speaking. After thirty seconds or so, Solo cut him off.
“You’ve made your point.”
Chewie chuckled.
“We came back to help the kid.”
A snort.
“That was not all about a reward.”
Another snort.

_{^{Smuggler's Run: A Han Solo & Chewbacca Adventure}}