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The warlock's Armor of Shadows eldritch invocation (PHB, p. 110) says:

You can cast mage armor on yourself at will, without expending a spell slot or material components.

The School of Abjuration wizard's 2nd-level Arcane Ward class feature (PHB, p. 115) says:

When you cast an abjuration spell of 1st level or higher, you can simultaneously use a strand of the spell’s magic to create a magical ward on yourself that lasts until you finish a long rest. The ward has a hit point maximum equal to twice your wizard level + your Intelligence modifier. Whenever you take damage, the ward takes the damage instead. If this damage reduces the ward to 0 hit points, you take any remaining damage.

While the ward has 0 hit points, it can’t absorb damage, but its magic remains. Whenever you cast an abjuration spell of 1st level or higher, the ward regains a number of hit points equal to twice the level of the spell.

Mage armor is an abjuration spell.

Can a warlock/abjuration wizard with the Armor of Shadows invocation proc Arcane Ward at will?

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    \$\begingroup\$ You don't even need to multiclass. If you're a level 18 Wizard, you also have a few at-will spells, and Mage Armor can be one of them \$\endgroup\$ – BlueMoon93 Aug 21 '18 at 9:49
  • \$\begingroup\$ @BlueMoon93 That's a really good point! I'm adding that to my answer. \$\endgroup\$ – NathanS Aug 21 '18 at 10:16
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Yes, this would work

The Arcane Ward class feature of the Abjuration Wizard does not specify that the abjuration spell in question has to come from a Wizard spell, nor does it mention spell slots, simply the spell's level, so as long as it's not a cantrip, if you find a way to cast an abjuration spell of 1st level or higher at will (such as by casting mage armor via the Armor of Shadows Eldritch Invocation) then your plan will work. You would be able to repeatedly cast mage armor in this way to restore the ward's hit points to the maximum amount "for free".

From the PHB, page 115:

Arcane Ward

Starting at 2nd level, when you cast an abjuration spell of 1st level or higher, you can simultaneously use a strand of the spell's magic to create a magical ward on yourself that lasts until you finish a long rest. The ward has hit points equal to twice your wizard level + your Intelligence modifier. Whenever you take damage, the ward takes the damage instead. If this damage reduces the ward to 0 hit points, you take any remaining damage.

While the ward has 0 hit points, it can't absorb damage. but its magic remains. Whenever you cast an abjuration spell of 1st level or higher, the ward regains a number of hit points equal to twice the level of the spell.


Without Multiclassing

As pointed out in a comment by @BlueMoon93:

You don't even need to multiclass. If you're a level 18 Wizard, you also have a few at-will spells, and Mage Armor can be one of them

So through the use of the Spell Mastery class feature of the Wizard, you can pick an Abjuration spell as your 1st level spell or your 2nd level spell and cast that at will to restore your Arcane Ward's hit point.

From the PHB, page 115:

Spell Mastery

At 18th level, you have achieved such mastery over certain spells that you can cast them at will. Choose a 1st-level spell and a 2nd-level spell that are in your spellbook. You can cast those spells at their lowest level without expending a spell slot when you have them prepared. [...]

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    \$\begingroup\$ This means you could restore your ward to full hp whenever you want, correct? All you would need to do is cast mage armor another couple times (for 2 hp per cast) \$\endgroup\$ – Riker Aug 18 '18 at 21:45
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    \$\begingroup\$ But that's not "temporary hp" really, it's just the ward taking the damage to its (real) hp. I think the rules distinguish between that and temp hp. \$\endgroup\$ – Riker Aug 18 '18 at 21:48
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    \$\begingroup\$ It's already distinguished in the wording: "The ward has hit points equal to...". Otherwise it would have said, "You gain temporary hit points equal to..." \$\endgroup\$ – Lino Frank Ciaralli Aug 18 '18 at 22:28
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    \$\begingroup\$ You're right. I will update my answer to make Riker's point explicitly. \$\endgroup\$ – NathanS Aug 18 '18 at 23:02
  • \$\begingroup\$ I feel like it could be up to the DM's discretion. It seems reasonable for the DM to say no on the basis of the ward needing you to "cast a spell of 1st level or higher" but you're not expending a spell slot when you cast Mage Armor. \$\endgroup\$ – J Nason Oct 11 '18 at 1:01

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