diff --git a/RELEASE-NOTES-next b/RELEASE-NOTES-next
index 78984c8a3..2d64c7d01 100644
--- a/RELEASE-NOTES-next
+++ b/RELEASE-NOTES-next
@@ -43,3 +43,4 @@ working. Please reach out to us in that case!
   • build: fix issues with parallel build
   • set _NET_DESKTOP_VIEWPORT after randr changes
   • fix a bug with i3-nagbar not starting after it has already started once
+  • fix conflict when moving parent of fullscreen window to workspace
diff --git a/src/con.c b/src/con.c
index 645d14486..3621c6624 100644
--- a/src/con.c
+++ b/src/con.c
@@ -1261,9 +1261,17 @@ static bool _con_move_to_con(Con *con, Con *target, bool behind_focused, bool fi
     }
 
     /* If moving a fullscreen container and the destination already has a
-     * fullscreen window on it, un-fullscreen the target's fullscreen con. */
+     * fullscreen window on it, un-fullscreen the target's fullscreen con.
+     * con->fullscreen_mode is not enough in some edge cases:
+     * 1. con is CT_FLOATING_CON, child is fullscreen.
+     * 2. con is the parent of a fullscreen container, can be triggered by
+     * moving the parent with command criteria.
+     */
     Con *fullscreen = con_get_fullscreen_con(target_ws, CF_OUTPUT);
-    if (con->fullscreen_mode != CF_NONE && fullscreen != NULL) {
+    const bool con_has_fullscreen = con->fullscreen_mode != CF_NONE ||
+                                    con_get_fullscreen_con(con, CF_GLOBAL) ||
+                                    con_get_fullscreen_con(con, CF_OUTPUT);
+    if (con_has_fullscreen && fullscreen != NULL) {
         con_toggle_fullscreen(fullscreen, CF_OUTPUT);
         fullscreen = NULL;
     }
diff --git a/testcases/t/132-move-workspace.t b/testcases/t/132-move-workspace.t
index 60705f96d..c7721c3d2 100644
--- a/testcases/t/132-move-workspace.t
+++ b/testcases/t/132-move-workspace.t
@@ -339,6 +339,53 @@ $ws = get_ws($tmp2);
 is_num_children($tmp2, 0, 'no regular nodes on second workspace');
 is(@{$ws->{floating_nodes}}, 1, 'one floating node on second workspace');
 
+###################################################################
+# Test that when moving a fullscreen floating window to a workspace
+# that already has an other fullscreen container, the second
+# container gets un-fullscreened.
+# See #4124
+###################################################################
+$tmp2 = fresh_workspace;
+$second = open_window;
+cmd 'fullscreen enable';
+$ws = get_ws($tmp2);
+is($ws->{nodes}->[0]->{fullscreen_mode}, 1, 'sanity check: fullscreen enabled');
+
+$tmp = fresh_workspace;
+$first = open_window;
+cmd 'floating enable, fullscreen enable';
+cmd "move workspace $tmp2";
+
+$ws = get_ws($tmp2);
+is_num_children($tmp2, 1, 'one regular node on second workspace');
+is_num_fullscreen($tmp2, 1, 'one fullscreen node on second workspace');
+is(@{$ws->{floating_nodes}}, 1, 'one floating node on second workspace');
+is($ws->{nodes}->[0]->{fullscreen_mode}, 0, 'previous fullscreen disabled');
+
+###################################################################
+# Same as above, but trigger the bug with the parent of a
+# fullscreen container, instead of a CT_FLOATING_CON.
+###################################################################
+$tmp2 = fresh_workspace;
+$second = open_window;
+cmd 'fullscreen enable';
+$ws = get_ws($tmp2);
+is($ws->{nodes}->[0]->{fullscreen_mode}, 1, 'sanity check: fullscreen enabled');
+
+$tmp = fresh_workspace;
+open_window;
+$first = open_window;
+cmd 'layout tabbed';
+cmd 'focus parent, mark a, focus child';
+cmd 'fullscreen enable';
+cmd "[con_mark=a] move workspace $tmp2";
+
+$ws = get_ws($tmp2);
+is(sum_nodes(get_ws_content($tmp2)), 4, '3 leafs & 1 split node in second workspace');
+# is_num_fullscreen does not catch this nested fullscreen container
+is($ws->{nodes}->[0]->{fullscreen_mode}, 0, 'previous fullscreen disabled');
+is($ws->{nodes}->[1]->{nodes}->[1]->{fullscreen_mode}, 1, 'nested fullscreen from moved container preserved');
+
 ###################################################################
 # Check that moving an empty workspace using criteria doesn't
 # create unfocused empty workspace.