[RPG] Can a sorcerer use a scroll of a spell not known

First question: trigger

The character needs only to have at least one level of a class which can cast the spell. In this case a first level wizard will be able to trigger any wizard spell.

Second question: completion

From the SRD: Scrolls

To have any chance of activating a scroll spell, the scroll user must meet the following requirements.

• The spell must be of the correct type (arcane or divine). Arcane spellcasters (wizards, sorcerers, and bards) can only use scrolls containing arcane spells, and divine spellcasters (clerics, druids, paladins, and rangers) can only use scrolls containing divine spells. (The type of scroll a character creates is also determined by his class.)
• The user must have the spell on her class list.
• The user must have the requisite ability score. If the user meets all the requirements noted above, and her caster level is at least equal to the spell's caster level, she can automatically activate the spell without a check.

This means that the character must be a spell caster of the correct type (arcane or divine): so no a fighter will not be able to use a scroll.

If she meets all three requirements but her own caster level is lower than the scroll spell's caster level, then she has to make a caster level check (DC = scroll's caster level + 1) to cast the spell successfully.

In this case: yes a first level wizard will be able to try with any arcane scroll (if he has the required Int) but he will have to perform an appropriate caster level with the following consequences:

If she fails, she must make a DC 5 Wisdom check to avoid a mishap (see Scroll Mishaps). A natural roll of 1 always fails, whatever the modifiers. Activating a scroll is a standard action (or the spell's casting time, whichever is longer) and it provokes attacks of opportunity exactly as casting a spell does.

Use magic device

You can use this skill to read a spell or to activate a magic item. Use Magic Device lets you use a magic item as if you had the spell ability or class features of another class, as if you were a different race, or as if you were of a different alignment.

This allow to override the first condition: even if you are not of the correct class (or have the wrong alignment and so on) and you have the use magic device skill you can do a check and try anyway.

So in this case if your 20th level fighter is trained in use magic device: yes he can use a scroll

At first, I agreed with the other answers, but a careful reading of the rules relating to adding a spell to a wizard's spellbook makes me believe that, by RAW, what your player suggests is correct.

This is mainly from two points:

1. Bull's Strength is a 2nd level wizard spell, so it exists on the Wizard spell list.
2. There is no mention in the spellbook scribing rules of having to meet the scroll's prerequisites.

Adding spells to a wizard's spellbook

There are only 3 restrictions listed in the above link:

1. The spell must be on the Wizard class spell list.
2. The Wizard must 'understand' the scroll (which he automatically does, since he scribed it).
3. The Wizard must study the scroll for an hour and make a successful spellcraft check.

As long as those three requirements are met, the Wizard can begin the scribing process. This wouldn't work for scrolls of Cure Light Wounds, or other spells that aren't on the Wizard spell list, but for Bull's Strength it should work without a problem.

In addition, this isn't really a powerful tactic. At most, the player is saving the gold price of half a scroll, and is getting assured access to some spells. Honestly, I can't think of a rules or balance reason not to allow this. It's not much more powerful than allowing wizards in the party to share spells out of their spellbooks.