SYMPTOM:
In Strategy Web 9.4.1 and above, the informative message below appears when a particular user tries to save objects into a Shared Reports children folder:

Error in save as (You do not have Write access to the Folder object 'Reports'.)

This issue started happening after clicking on the Update ACLs For Reports option, available in Strategy Desktop by clicking on Project Configuration > Project Definition > Security, under Security model, as shown:

It is described in the Strategy technical note below an issue that is quite similar; however, at this time, the affected user's group was listed in the Parent folder ACL list:
CAUSE:
Upon reviewing the Public Folder Security options, it was found that subfolders were not inheriting the parent's ACL configuration; therefore, the newer Shared Reports children folders had different permissions.
ACTION:
Follow the steps below to avoid this scenario and propagate the parent's folder ACL configuration to its subfolders:
1) In Strategy Desktop, right mouse click on the Public Objects > Reports folder and select Properties
2) Click on Security, so enable the options:
a) Apply changes in permissions to all children objects. (This option is intended to propagate all permissions changes to the children folders)
b) Overwrite children’s access control lists. (This option is intended to overwrite the ACL from all children folders)
c) Recursively. (This option is intended to propagate changes on the parent's folders to be applied on all children folders recursively, up to the latest level from top to down)
NOTE: For further information regarding the Update ACL For Reports option, refer to the Strategy technical note: