Question: In a cross-genre game, is there a spell/power that a mage can use to heal a vampire?

I’ve looked through the mage spells in Death and Life but neither show how a vampire can be healed.

Answer: 
**Temporal Summoning**

At the page 190 of Mage the Awakened's second edition there is a spell called Temporal Summoning. The spell description reads 

> 
> Return the subject to an younger version of itself. Buildings can be restored and injuries healed. Once the spell ends any changed made revert back to normal. Any injuries and Conditions obtained while this spell was active carry over to the subjects present self. Limits of Spell includes not being able to bring the dead back and a vampire returned to 'Childhood' becomes a vampiric child 
> 
> 
> 

Other than this there is also a spell called Shared Fate at Page 137 which reads

> 
> Two or more subjects are bound together. Any damage, Tilt or Condition suffered by one will also affect the other
>  +1 Reach: Link is only one way
>  +2 Reach: Subject is not linked to any other subjects. Instead, she suffers any damage, Tilt or Condition she inflicts on others 
> 
> 
> 

If you were to connect yourself to a vampire and gain a condition that heals you then by extension the vampire would be healed.
Apart from the two rotes above you always have

Creative Taumaturgy
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> 
> Within the bounds of their power, mages can conjure nearly any effect they can imagine. (MtA2 p125)
> 
> 
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The practice for healing is **Perfecting**

> 
> Perfecting spells are the opposite of Fraying spells in many
>  ways: they bolster, strengthen, and improve rather than
>  weakening and eroding. A Perfecting spell might repair
>  damage to an object or a person (Matter or Life)... (MtA2 p123)
> 
> 
> 

Now you have the opportunity of turning this into a 

Mystery
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> 
> Any magical puzzle, any lingering spell, any otherworldly
>  enigma is potentially a Mystery. The Storyteller decides on the
>  particulars of the Mystery, which break down into three parts:
>  Opacity, surface information, and deep information. (MtA2 p93)
> 
> 
> 

The Mage could Scrutinize the Mystery of the vampiric condition to design the imago to heal a vampire.

In my games the spell required Arcana imho would be Matter 3 (to repair the structure of the corpse) and Death 2 (to redirect the flow of death that powers it).

But you could argue that a different combination makes more sense (Life instead of Death, or even Prime), perhaps depending on the nature of the damage, or depending on how well the Mage unveils the Mystery, or depending on what suits your game better.