How do I change all double-spaced sentence endings with single-spaced ones?

I am a writer and have always used double spaces between sentences and am now informed that the publishers, to whom I submit my stories and such, prefer single spaces there. This is a significant challenge even in a short story, let alone a novel. I have tried the regular search & replace procedure but find it won’t accept spaces with no text. Any suggestions?

Find: <two spaces>

Replace: <one space>

Replace all.

Done.

What exactly is the problem, if any?

It’s about the term “sentence ending”. In what places can occur double spaces in your document which you NOT want to be replaced by single spaces? Can you describe what you mean by “sentence ending” precisely? (Don’t forget to consider quotes, e.g.)
If you consider to resort to user code: The API has a sentence cursor. (F&R has no respective means.)

In addition to @gabix’s suggestion: no need to tick “Regular expression”; all are regular characters.

If you didn’t tick in Tools > AutoCorrect > AutoCorrect Options > Options the option Ignore double spaces then all your carefully crafted double spaces will have been converted to single spaces as you typed. Find and Replace would have nothing to find.

Click View > Formatting marks to see if you actually have any double spaces.