
Spoiler
He died an unfated death in the first timeline and in the afterlife he asked the Angel for memories in the next life. When a person dies an unfated death, they get to make wishes when they meet the Angel in the temporary afterlife. It’s temporary because people who die an unfated death always get a chance to relive their lives to meet their proper fated death. So when Oscar married Ines, he actually had memories of the previous timeline before that one. He claims part of his horrible treatment of Ines was because of old scores in the previous timeline.
After the timeline where he was married to Ines and she committed suicide, he also committed suicide because he was being mercilessly tortured every day. In the timeline when Ines ran away, he had his memories from the previous timeline just like Ines had hers. In that timeline, he committed suicide to follow Ines into the next life. He had already figured out that suicide allows the person to retain their memories of the previous timeline. He also knows this timeline is the last timeline for Ines so he’s once again biding his time to reclaim her.

Huge Spoiler (from novel spoiler)
If you like surprise from plot twists, DO NOT READ
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Just adding some more seasoning to OP...
Ines first life wasn't actually her marriage with the prince, but with Carcel. They were happily married and had children T^T
But the prince was jealous of Carcel and can't stand seeing Carcel happy so he wanted Ines. Stuff happened, he killed himself, which led to the 2nd timeline, where he married Ines. In the novel, 3 people remembered their lives starting from their s***ide timeline

Correction:
The prince didn’t kill himself in the true first timeline. He was publicly executed by the citizens led by Ines’s brother who put another prince on the throne because Oscar abused his authority. This happened after Carcel and Ines were already dead at the young age of 28. The prince was never meant to die in that particular manhwa instigated by Ines’s brother so his death was unfated. The main villain in the first timeline is actually a woman and not Oscar.

There are two antagonists. Spoiler
The female is considered the worst by some novel readers. Personally I agree as well. Nevertheless, both of them are Ines and Carcel’s enemies. Oscar wants Carcel dead so he can get Ines and the villainess wants to trample all over Ines, make her infertile and subservient to her.
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Spoiler
The villainess is the one who started everything. She hates Ines with a passion. She poisoned her from the young age of 16. She wanted to destroy Ines’s happiness and she succeeded in killing the children Ines gave birth to and killing Ines in the process. Ines was terminally ill for many years and devastating physical pain so much that she would cry and beg for death.
The last five years of her life were the best because Carcel brought her to Calztela, bought the small house atop Logorño Hill and poured all his care and love into her life. He took a demotion on his job and spent his time personally nursing Ines back to some semblance of health. There’s nothing he didn’t do for her as her husband including wiping her down every day, cleaning her up when she urinated and more, brushed her teeth, and kept her clean and dignified.
After Ines finally was able to walk again and got healthy, the emperor kept pressuring Carcel to go to war to save their fleet and navy men that were losing the war. Carcel went to war and came back injured but had succeeded in turning the war around and saving Ortega’s face.
However, even while he was injured and confined to his home to recover, Oscar and another country’s crown prince got into trouble. While they were drunk and having a sexual orgy with women, Oscar accidentally shot and killed the foreign prince. This forced Carcel to go to war while injured. Ines was very upset because she felt that he would die. There was nothing she could do about it so instead she prayed that if he die on the battlefield, she wanted to finally die as well. The priest who was an angel in disguise honored her prayer and so when Carcel did end up dying on the battlefield, Ines died in the same moment. They both died at the same time and same age.
It’s also hinted that in this current life, they will both die together as well after living into their old age.
The crown prince has memories of the past too