Short answer: No — the Major V Earcushion (2 Stk) are designed for the Major V and are not specified as compatible with the Major III.
Details: Marshall lists distinct ear‑cushion spare parts for Major IV and Major V separately and offers a specific Major V ear‑cushion SKU, while Major III replacements are treated separately by third‑party sellers and guides, indicating model‑specific fit and slight shape differences between Major generations. User guides and teardown/replacement videos note ear‑pad designs and mounting can differ across Major II/III/IV/V and that pads are not always directly interchangeable without modification.
If you need pads for Major III, choose parts listed for Major III to ensure correct fit; I'm not completely certain if a physical modification could allow Major V cushions to fit because official sources do not state compatibility between Major V and Major III.