diff --git a/firedrake/mg/ufl_utils.py b/firedrake/mg/ufl_utils.py
index 0408a6d2a6..02649b57b9 100644
--- a/firedrake/mg/ufl_utils.py
+++ b/firedrake/mg/ufl_utils.py
@@ -268,6 +268,8 @@ def coarsen_snescontext(context, self, coefficient_mapping=None):
     coarse._fine = context
     context._coarse = coarse
 
+    solutiondm = context._problem.u.function_space().dm
+    parentdm = get_parent(solutiondm)
     # Now that we have the coarse snescontext, push it to the coarsened DMs
     # Otherwise they won't have the right transfer manager when they are
     # coarsened in turn
@@ -275,13 +277,12 @@ def coarsen_snescontext(context, self, coefficient_mapping=None):
         if isinstance(val, (firedrake.Function, firedrake.Cofunction)):
             V = val.function_space()
             coarseneddm = V.dm
-            parentdm = get_parent(context._problem.u.function_space().dm)
 
             # Now attach the hook to the parent DM
             if get_appctx(coarseneddm) is None:
                 push_appctx(coarseneddm, coarse)
-                teardown = partial(pop_appctx, coarseneddm, coarse)
-                add_hook(parentdm, teardown=teardown)
+                if parentdm.getAttr("__setup_hooks__"):
+                    add_hook(parentdm, teardown=partial(pop_appctx, coarseneddm, coarse))
 
     ises = problem.J.arguments()[0].function_space()._ises
     coarse._nullspace = self(context._nullspace, self, coefficient_mapping=coefficient_mapping)
@@ -384,7 +385,8 @@ def create_interpolation(dmc, dmf):
     mat.setType(mat.Type.PYTHON)
     mat.setPythonContext(ctx)
     mat.setUp()
-    return mat, None
+    rscale = mat.createVecLeft() if row_size == col_size else None
+    return mat, rscale
 
 
 def create_injection(dmc, dmf):
diff --git a/tests/multigrid/test_transfer_manager.py b/tests/multigrid/test_transfer_manager.py
index d11bceb41f..a3049af242 100644
--- a/tests/multigrid/test_transfer_manager.py
+++ b/tests/multigrid/test_transfer_manager.py
@@ -1,5 +1,6 @@
 import pytest
 import numpy
+import warnings
 from firedrake import *
 from firedrake.mg.ufl_utils import coarsen
 from firedrake.utils import complex_mode
@@ -131,3 +132,25 @@ def test_transfer_manager_dat_version_cache(action, transfer_op, spaces):
 
     else:
         raise ValueError(f"Unrecognized action {action}")
+
+
+@pytest.mark.parametrize("family, degree", [("CG", 1), ("R", 0)])
+def test_cached_transfer(family, degree):
+    # Test that we can properly reuse transfers within solve
+    sp = {"mat_type": "matfree",
+          "pc_type": "mg",
+          "mg_coarse_pc_type": "none",
+          "mg_levels_pc_type": "none"}
+
+    base = UnitSquareMesh(1, 1)
+    hierarchy = MeshHierarchy(base, 3)
+    mesh = hierarchy[-1]
+
+    V = FunctionSpace(mesh, family, degree)
+    u = Function(V)
+    F = inner(u - 1, TestFunction(V)) * dx
+
+    # This test will fail if we raise this warning
+    with warnings.catch_warnings():
+        warnings.filterwarnings("error", "Creating new TransferManager", RuntimeWarning)
+        solve(F == 0, u, solver_parameters=sp)