Giving read write access to different PC?

I have an old MBL 2TB and I can only access it with both read and write with an old laptop that is about to die. I need to transfer access to a new laptop as well as a desktop. How do I do this? I cna see the drive on both new computers and can copy from the MBL to the computer but I cant upload from the new computer to the MBL.

Any ideas?

This is a Windows file management issue, not a drive issue. Google to learn how to set/change properties of read/write access for files on any drive; WD or otherwise.