The starter in that last Aldi mower image is a Sanli starter or a Victa V40 starter as they are the same starter Mf.
Mw, How do you test that it will grip the cup?
hold the starter in the cup and pull the starter rope to make sure it grips the starter cup .You can usually see if
it's going to grip the cup.
I have changed a lot of starter cups with different starters as sometimes you need a lower starter cup , but I
don't remember what cup I used with that last Aldi mower image as it was from a few years ago but I remember using a few
Tecumseh starter cups with non Tecumseh starters so may be a Tecumseh cup ,that's if the Aldi Cup won't work.
I'd just use whatever starter and cup that will fit even with an adapter plate but I haven't used the side Valve Briggs
starter with the Aldi mower because I had other starters to use up.
Cheers
Max.