Maybe this will work for you (not tested!):
$SourceDir ="C:\Users\StandardUser\AppData\Roaming\Mozilla\Firefox\Profiles"
$DestinationDir = "C:\FireFox\"
$FileNameAndExtension = "places.sqlite"
Get-Childitem –Path "$SourceDir" -Include "$FileNameAndExtension" -File -Recurse | Copy-Item -Destination "$DestinationDir"
(If the reply was helpful please don't forget to upvote and/or accept as answer, thank you)
Regards
Andreas Baumgarten