Can't set up a network printer

[McBugzz]

I've got the following setup:

One computer with an internet connection, and a printer. The other computer is directly connected to it via 100 MBit LAN. Both use WinXP Pro.

I have organized a workgroup and declared the printer as shared. The problem is - for some reason the first computer has no problems accessing the second one, but not vice versa. Until I explicitly try to connect to the first from the second (by loggin in as administrator of the first computer) I can't use the printer. Says I have not enough rights.

 

[bcastner]

Add the usernames and passwords of Coputer B as new usernames and passwords on Computer A.
Add the usernames and passwords of Coputer A as new usernames and passwords on Computer B.