How does Find Familiar work with a Ring of Spell Storing?

Question

Say a Wizard casts Find Familiar for himself, and then casts it again into a Ring of Spell Storing. The Ring is then given to another person, let's say a Rogue, who uses the Ring to cast Find Familiar.

The description of Find Familiar says

If you cast this spell while you already have a familiar, you instead cause it to adopt a new form.

but the description of the Ring says

The spell has no effect, other than to be stored in the ring.

What happens? Does the Wizard's familiar change when the spell is cast into the Ring? Does it change when the spell is cast out of the Ring? Does the Rogue get a Familiar, since the Rogue is considered to be casting the spell?

Answer 1

Specific Overrides General

This is a basic "specific overrides general" situation. The Ring of Spell Storing has specific rules that override the general cases for Find Familiar.

When the wizard loads the ring, the specific case of "Casting Find Familiar into a Ring of Spell Storing" overrides the general case of "Casting Find Familiar".

The clause...

the spell has no effect, other than to be stored in the ring

...trumps anything the spell might do otherwise.

When the rogue activates the ring, the specific case of "Casting Find Familiar from a Ring of Spell Storing" overrides the general case of "Casting Find Familiar".

The spell uses the slot level, spell save DC, spell attack bonus, and spellcasting ability of the original caster, but is otherwise treated as if you cast the spell.

...means the Rogue is the caster and gains the familiar, even though the wizard's stats are used. The stats are not really relevant for the spell in question, but it may matter for other spells.

End Result

The Rogue gains a familiar. If it somehow already had one, it changes or reappears as described in the spell.

Side Note

The ring can be loaded by "any creature", but actually using the ring to cast a spell requires attunement.

Answer 2

The Rogue gains a familiar

As noted in the description of The Ring of Spell Storing (emphasis mine):

The spell uses the slot level, spell save DC, spell attack bonus, and spellcasting ability of the original caster, but is otherwise treated as if you cast the spell.

As you have noted, Find Familiar states:

If you cast this spell while you already have a familiar, you instead cause it to adopt a new form.

The "you" in the spell description refers to the caster of the spell. Any spell cast from the ring acts as if the wearer, in this case the rogue, is the caster. Therefore, if the rogue has no familiar, it gains one of its own.

It's worth noting that if the rogue had a familiar before this point (say from the Arcane Trickster archetype), then the familiar will either reappear (if it had previously been reduced to 0 hit points) or it will change form if it already exists based on the rules provided by the Find Familiar spell.