You can copy preserving the modification time, e.g.,
cp --preserve=timestamps source destination
or (more generally: mode, ownership and timestamps)
cp -p source destination
although in some cases, preserving ownership is not wanted.
Similarly, you can copy to remote systems using scp's
scp -p source remote:destination
scp does not have separate options for the mode, etc. Since it runs with the given remote permissions, it does not have a feature for setting remote ownership at the same time. Because of these limitations, you might want to use
tar to make an archive which you extract on the remote system, preserving as much information as possible.
The ELF format used for binary files does not include a date, so the file's modification timestamp is all that you can preserve.