If a cleric wrote a scroll of a spell that a wizard can learn, could a wizard learn the spell?

Question

When a cleric would write a scroll of a spell that a wizard could cast like Protection from Evil and Good, would the wizard be able to learn the spell from the Cleric scroll?

Answer 1

This can work.

Wizards don't learn spells; they copy them to their spellbooks and prepare them. But besides this small detail, your scenario would work, if the following criteria are met. (This answer assumes that the optional rules for Scribing a Spell Scroll from Xanathar's Guide to Everything will be followed.)

1. The DM must allow the scribing of spell scrolls.
2. The spell in question must be on both the cleric and wizard spell lists (protection from evil and good meets this criterion).
3. The cleric must have proficiency in the Arcana skill.
4. The cleric must have the spell in question prepared.
5. The cleric must spend the necessary downtime and gold to scribe the spell scroll.
6. The wizard must succeed on the necessary Intelligence check to copy the spell from the scroll.
7. The wizard must spend the necessary downtime and gold to copy the spell to their spellbook.

Sources:

1. Scribing a Spell Scroll downtime activity description from Xanathar's Guide to Everything ch. 2
2. Spell scroll magic item description from Dungeon Master's Guide ch. 7
3. Wizard spellbook description from Player's Handbook ch. 3

Addendum: Ryan C. Thompson points out that in lieu of the Scribing a Spell Scroll rules from Xanathar's Guide to Everything, the Crafting a Magic Item rules from the Dungeon Master's Guide could also be used to create a spell scroll. Those rules would replace my points 3 through 5 above. Both sets of rules are optional and subject to DM allowance.

Answer 2

A spell on a scroll is on your list or it isn’t

If it is, you can use it.
If it isn’t, you can’t.
How it got to be on a scroll is entirely irrelevant.