Q: shared folder with read and write access but file says read only

Select the folder, choose Get Info from the File menu, unlock the Sharing & Permissions section, click on the gear, and choose to apply the settings to the enclosed items.

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This fixed it the first time and the person to whom I gave permission was able to change and save it.  Then when I (the administrator and originator of the document) tried to make changes on the new saved document, it said it was "Read Only".  I had to go back and give myself the Read/Write permission.  It seems that every time the document is changed/saved, you have to repeat giving Read/Write permission to ALL with permission to view the "Shared" folder.  Anyway to give everyone access to the Shared folder permanent Read/Write permission that will not revoke the Write permission each time the document is changed?

Try changing Everyone to read/write.

Thanks Eric.  That didn't work exactly but helped me to find a solution. Summary:  I set up the Shared Folder on my iMac and gave my wife (and Everyone) permission to Read & Write all the files in that folder.  She can successfully access and change them from her MacBook.  Then, when I later open the document (newly changed by her) and click on Get Info, I see that my name is no longer listed in the Sharing & Permissions window.  After adding myself back to the list I am able to again make changes to the document and save it to the Shared Folder.  My wife likewise can re-open the file I changed and still has Read & Write access again, too.  Strange, but it appears that after she changes the document my name is removed from "Sharing & Permissions" even though I am the Author of the document and owner/Administrator of the Shared Folder.  As a side note, when she goes to "Get Info" on the documents, Under "Sharing & Permissions", it only says "You have custom access".  There is no box there to allow her to see/change the priveleges so she cannot add me.  I hope this has helped you and others.  If you know/think of an easier, permanent fix where I don't have to add myself and reset permission each time she alters the file; that would be great.