Find files belonging to a group

Assuming you have your desired files in a text file, you could do something like

while IFS= read -r file; do 
    echo mkdir -p ${file%/*}; 
    cp /source/"$file" /target/${file%/*}/${file##*/}; 
done < files.txt 

That will read each line of your list, extract the directory and the file name, create the directory and copy the file. You will need to change source and target to the actual parent directories you are using. For example, to copy /foo/a/a.txt to /bar/a/a.txt, change source to foo and target to bar.

I can't tell from your question whether you want to copy all directories and then only specific files or if you just want the directories that will contain files. The solution above will only create the necessary directories. If you want to create all of them, use

find /source -type d -exec mkdir -p {} /target

That will create the directories. Once those are there, just copy the files:

while IFS= read -r file; do 
    cp /source/"$file" /target/"$file"
done

Update

This little script will move all the files modified after September 8. It assumes the GNU versions of find and touch. Assuming you're using Linux, that's what you will have.

#!/usr/bin/env bash    

## Create a file to compare against.
tmp=$(mktemp)
touch -d "September 8" "$tmp"

## Define the source and target parent directories
source=/path/to/source
target=/path/to/target

## move to the source directory
cd "$source"

## Find the files that were modified more recently than $tmp and copy them
find ./ -type f -newer "$tmp" -printf "%h %p\0" | 
    while IFS= read -rd '' path file; do
        mkdir -p "$target"/"$path"
        cp "$file" "$target"/"$path"
    done

Strictly speaking, you don't need the tmp file. However, this way, the same script will work tomorrow. Otherwise, if you use find's -mtime, you would have to calculate the right date every day.

Another approach would be to first find the directories, create them in the target and then copy the files:

1. Create all directories

    find ./ -type d -exec mkdir -p ../bar/{} \;
   

2. Find and copy the relevant files

    find ./ -type f -newer "$tmp" -exec cp {} /path/to/target/bar/{} \;
   

3. Remove any empty directories

    find ../bar/ -type d -exec rmdir {} \;
   

Traditional unix permissions only allow user, group, other permissions as you've found. These can result in some awkward combination of groups needing to be created...

So a new form of ACL (Access Control Lists) were tacked on. This allows you to specify multiple users and multiple groups with different permissions. These are set with the setfacl command and read with getfacl

$ setfacl -m u:root:r-- file.txt
$ setfacl -m u:bin:-wx file.txt 
$ setfacl -m u:lp:--x file.txt 
$ getfacl file.txt
# file: file.txt
# owner: sweh
# group: sweh
user::rw-
user:root:r--
user:bin:-wx
user:lp:--x
group::r--
mask::rwx
other::r--

You can easily tell if a file has an ACL by looking at the ls output:

$ ls -l file.txt
-rw-rwxr--+ 1 sweh sweh 0 Jul 26 10:33 file.txt

The + at the end of the permissions indicates an ACL.