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The phrase "resolution to the" is correct and usable in written English in certain contexts.
For example, you might use it in the following sentence: "He offered an effective resolution to the long-standing conflict." Here, "resolution" refers to a solution.
Exact(60)
"It's a good resolution to the problem".
The final resolution to the matter remains unclear.
An immediate resolution to the state's problems is not apparent.
Mr. Malik called on a peaceful resolution to the crisis.
Analysts foresaw no quick resolution to the standoff.
A resolution to the nuclear crisis, however, requires pragmatic engagement.
A quick resolution to the war, though, could change the situation, he said.
The talks are intended to bring a quick resolution to the civil claims against Andersen.
But Spanish officials said they hoped for a quick resolution to the conflict.
"His willingness to repay that made this a fair and just resolution to the case".
However, arresting criminals and removing their threat [would be] the ultimate resolution to the matter".
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com