By default, an arcane trickster cannot use an arcane focus to cast their spells, as they lack the class feature that wizards and warlocks have that allows them to; this forces them to use a component pouch for their material needs.
However, as a wizard "can use an arcane focus as a casting focus for their wizard spells" and the spells arcane tricksters learn are repeatedly referred to as "wizard spells", can an arcane trickster/wizard multiclass use an arcane focus for the spells which they learnt from being an arcane trickster?
It may be useful to note that both arcane tricksters and wizards have exactly the same spell-casting text:
'Intelligence is your spell-casting ability for your wizard spells, since you learn your spells through dedicated study and memorization.'
This seems to imply that they cast their spells in the same mannner.
Presumably the answer to this would also apply to an eldritch knight/wizard multi-class as well?
Best Answer
Yes, as long as you are multiclassed
Since the spells gained from the Arcane Trickster's Spellcasting feature are referred to as "wizard spells", these spells would qualify for the wizard's Spellcasting Focus feature as long as you have it.
(All emphasis mine)
Eldritch Knight?
Since the Eldritch Knight also uses similar language, the same rule applies.