script - Linux: Trying to find files from a list recursively and copy them somewhere else

I'm trying to find files from a list and copy them to another place. So I started my test loop like that:

# cat ~/my_filelist.txt | while read file ; do echo "$file" ; done

After I hit enter all filenames from my_filelist.txt are print to stdout, fine.

Now I replaced "echo" with "find" command like that:

# cat ~/my_filelist.txt | while read file ; do find . -name "$file" ; done 

I thought that find will print the results to stdout, but nothing happens O_o

I can see that find is working but where is the ouput?

Could somebody tell me what I'm doing wrong?

Many thanks in advance!