You need one user with the same password on both computers.
Explanation detailed follows.
You have:
computerA with users UserAA, UserAB, UserAC (I suppose we are talking about windows XP here)
computerB with users UserBA, User BB, UserBC
On computer B you have a share which you want to access from computerA and don't want to be asked username and password for that.
You can access the share on computerB (from computerA = from another computer in your network) if you know the password and the account name of one account from computerB and that user has access rights for reading the folder and access the share from network. And that password should NOT be blank, as far as I know Windows rejects the connection with blank passwords from network.
Another option is to enable user Guest and give him access to that share and read access to the shared folder (I don't recommend you this option).
But, in your case, I sugest to create the same account on both computers. Lets say CommonUser, with the same password (so you have CommonUser on computerA with password "zzz", and also you have the user CommonUser on computerB, with the password "zzz" = the same). And, when you want to access the share on the other computer, log in into Windows with that user (CommonUser). It won't ask a username and password now, if you want to access the share. But if you log in computerA with UserAA (which exists only on computerA), it will ask username and password when you try to access the share.
(I should make this explanation more simplist, but I don't know how...
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