As an ITIL user navigate to an open problem record and click on the incident related list, then click Edit.. button of the related list, then try associating a closed incident from the slushbucket. System just ignores the update, nothing happens on the form.
The following out of the box write ACL on incident record "sys_security_acl.do?sys_id=66ec26370a0a0b0100a67b597d415b84" has a condition as "Incident State is not Closed" and hence ITIL user is unable to associate a problem to the closed incident record.
However, admin would be able to associate problem to the closed incident, as the ACL's would be bypassed.
You need to remove the condition"Incident State is not Closed" from the following out of the box ACL to allow the ITIL users to associate the problem record to an closed incident record: "sys_security_acl.do?sys_id=66ec26370a0a0b0100a67b597d415b84"
This will be a straight forward change, but it involves modifying the out of the box ACL. Hence this is not a recommended approach as you might miss the updates on this ACL between the upgrades.
Other best approach is you can create a new write ACL as below,
Type = Record
Operation = Write
Active = true
Name = Incident
Field = None
Role = ITIL
Condition = Incident State is Closed