I had trouble with the most popular answer (overthinking). It put AFolder in the \Server\MyFolder\AFolder and I wanted the contents of AFolder and below in MyFolder. This didn't work.
Copy-Item -Verbose -Path C:\MyFolder\AFolder -Destination \\Server\MyFolder -recurse -Force
Plus I needed to Filter and only copy *.config files.
This didn't work, with "\*" because it did not recurse
Copy-Item -Verbose -Path C:\MyFolder\AFolder\* -Filter *.config -Destination \\Server\MyFolder -recurse -Force
I ended up lopping off the beginning of the path string, to get the childPath relative to where I was recursing from. This works for the use-case in question and went down many subdirectories, which some other solutions do not.
Get-Childitem -Path "$($sourcePath)/**/*.config" -Recurse |
ForEach-Object {
$childPath = "$_".substring($sourcePath.length+1)
$dest = "$($destPath)\$($childPath)" #this puts a \ between dest and child path
Copy-Item -Verbose -Path $_ -Destination $dest -Force
}