Quest items cannot be transferred to the offline stash. Logs show exception for every click of the transfer button:
2021-11-22 23:16:25.773 -05:00|0.12.11.7.15426|Error|Default|
EXCEPTION: System.NullReferenceException: Object reference not set to an instance of an object
at EFT.UI.TasksScreen.<Awake>b__49_7 () [0x0003c] in <570aae2fd612408b8d1519fd0b183c1e>:0
at UnityEngine.Events.InvokableCall.Invoke () [0x00010] in <309a05e2dd0a4e38aa2f0404a7fd287c>:0
at UnityEngine.Events.UnityEvent.Invoke () [0x00022] in <309a05e2dd0a4e38aa2f0404a7fd287c>:0
at EFT.UI.DefaultUIButton.method_11 () [0x0000a] in <570aae2fd612408b8d1519fd0b183c1e>:0
at EFT.UI.TweenAnimatedButton.OnPointerClick (UnityEngine.EventSystems.PointerEventData eventData) [0x00012] in <570aae2fd612408b8d1519fd0b183c1e>:0
at UnityEngine.EventSystems.ExecuteEvents.Execute (UnityEngine.EventSystems.IPointerClickHandler handler, UnityEngine.EventSystems.BaseEventData eventData) [0x00007] in <be0470fe00be4c1f9e13c0a38b4e167e>:0
at UnityEngine.EventSystems.ExecuteEvents.Execute[T] (UnityEngine.GameObject target, UnityEngine.EventSystems.BaseEventData eventData, UnityEngine.EventSystems.ExecuteEvents+EventFunction`1[T1] functor) [0x00063] in <be0470fe00be4c1f9e13c0a38b4e167e>:0