Step 1: The autopsy challenge in a sudden peripartum maternal death is to prove that fetal material has lodged in the mother's lungs. This requires histological stains that highlight squames, mucin and vernix.
Step 2: Phloxine-Tartrazine, named the Lendrum technique, selectively colours the keratinised fetal squamous cells trapped in pulmonary vessels, making it the signature stain for amniotic fluid embolism.
Step 3: Adjuncts round out the picture: Alcian Blue marks the mucin of fetal secretions and Sudan Black or Oil Red O marks the fatty vernix caseosa.
Step 4: Because air embolism relies on dissection or radiology and fat embolism on lipid stains of systemic tissue, neither calls for Lendrum stain, leaving amniotic fluid embolism as the match.
\[\boxed{\text{Amniotic fluid embolism}}\]