"to fill the emptiness within someone"

One of the senses of the word match.

It's a metaphor. When we have a pair of socks, for instance, we say each pair matches the other. They can complete only one another.

If two people who are having a relationship are a good match, they complete each other. e.g. Theirs is a match made in heaven (they are very suitable to each other)

Source: Cambridge Dictionary

A little more context in which you wish to place the word would be helpful but I suggest fulfil may be useful in sentences such as “After they met, he was fulfilled”.

Fulfil = to satisfy someone or to make someone feel happy

https://dictionary.cambridge.org/dictionary/english/fulfil

American spelling is fulfill

Here is a randomly selected example:

First, to truly understand men and how to make them feel fulfilled in a loving relationship, it is helpful to realize that men don’t just want love—they want to be respected.

Lifehack

I'm going for:

plenum

As in:

You are my plenum

Definitions:

a full assembly
the whole of space regarded as being filled with matter

Have you considered satiate?

having one's appetite completely satisfied (Websters)

To provide (someone) with more than enough. (American Heritage)

Related words include sate, sated, satiety