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The phrase "after we found" is correct and usable in written English.
You can use it to indicate a sequence of events where something was discovered or located prior to another action or event.
Example: "After we found the missing documents, we were able to complete the report on time."
Alternatives: "once we discovered" or "following our discovery".
Exact(55)
After we found out, we were all in shock.
We left them exposed after we found them.
"And then the next step will be after we found that out".
Shortly after, we found a dead baby woodchuck, apparently storm-drowned, in the yard.
Soon after, we found the second bone, also with a lot of marks on it.
We lingered peacefully even after we found the brass plaque marking the plain wooden pew where Franklin sat.
The project was launched by journalists in our US office after we found ourselves constantly defending 'Americanisms' in story threads.
Since 2014, after we found a machine that fit in the kitchen, we've been milling our own corn at Pujol.
It wasn't until after we found her sister's journal a few years ago that we knew what had happened.
Similar(2)
After we found the head, I started researching online and found an article about a family in Arlington who had discovered three decapitated fox heads in their yard in 2013.
"Right after we found out about Denise's cancer, it was such a shock for us — watching her go through all this stuff, that song just came out," he said.
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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