tl;dr
cp -R "/src/project 1/App" "/src/project 2"
Explanation:
Using quotes will cater for spaces in the directory names
cp -R "/src/project 1/App" "/src/project 2"
If the App directory is specified in the destination directory:
cp -R "/src/project 1/App" "/src/project 2/App"
and "/src/project 2/App" already exists the result will be "/src/project 2/App/App"
Best not to specify the directory copied in the destination so that the command can be repeated over and over with the expected result.
Inside a bash script:
cp -R "${1}/App" "${2}"