How to copy folder in UNIX with different owners and permissions to preserve it all in target location?

I need to copy folder from a to b.
The folder owned by user1 and have folders and files owned by both user1 and user2 inside of it in different locations.

I need to copy it and preserve the ownership and permissions (ownership more important).

I don't have root permissions, I can login with both users.

cp -a and copy -p didn't help, when I copy in any way it will get the ownership of which user I'm log in with.

Thank you for helping.

Let's say under a there's some file a/x/y that does not belong to you, user1, but rather belongs to user2.

You are trying to create a copy of a, b, such that b/x/y belongs to user2. Meaning, you are trying to create a file on someone else's behalf, and that is a security problem.

The OS will prevent you from doing that if you don't have root permissions. As mentioned in the comments, tar is the closest you can get - an archive that will remember the permissions such that when you do have permissions to create files on behalf of user2, it will remember what files they are.

If you're wondering why it's a security problem to create files on someone else's behalf, here's just 2 examples:

1. Admin sets per-user quotas. Every user gets N GB of disk space. user1 recreates the file a/x/y, under different file names, b/x/y1, b/x/y2, ..., on behalf of user2, in a loop, until the quota for user2 is exhausted. user1, who owns the directories b and b/x then runs chmod go-rwx b/x such that user2 can't even access the directory b/x to delete these files. user2 now can't write anything to disk.
2. user1 writes a program like su that changes its UID to root and runs /bin/bash. it creates a copy of it on behalf of (i.e. owned by) the root user, with mode r-s (read, write, setuid), which means that the program will succeed in changing its UID to root. Root shell achieved.