"remember better" is correct and usable in written English, usually as an imperative phrase.
For example, you might write: "Remember better for next year's exam!".
They remember better days gone by.
I think and remember better late, or imagine I do.
"I wish I could remember better," she said.
(But nobody likes a whiner, remember?) Better to learn from Mr. Mumbles's sad example.
Some of us remember better days for the team and the city.
But what I remember better many years later are the fine professors I met, my fellow students and campus life.
Personality sketch of John Sims Kelly, remembered better as Shipwreck Kelly.
For Murray remembers, better than most writers, the "grim de-dreamification" of growing up.
His hands are clasped behind his back, and Ms. Tucci imagines him remembering better times.
The New Yorker, October 9, 1937 P. 70 Personality sketch of John Sims Kelly, remembered better as Shipwreck Kelly.
Ms. Ansari was remembering better days before her husband lost his job, at a factory that made cardboard boxes.
