https://codex.www.ads-software.com/Hosting_WordPress
from the docs:
Server requirements
WordPress server requirements for versions prior to 2.0:
* PHP version 4.1 or greater
* MySQL version 3.23.23 or greater
WordPress server requirements for version 2.0:
* PHP version 4.2 or greater
* MySQL version 3.23.23 or greater
* (Optional) Apache mod_rewrite module (for clean URIs known as Permalinks)
Isnt that clear? (rhetorical question) Those are the requirements.It follows since it does not say APACHE, that APACHE is not a requirement.
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Recommended setup
We recommend Apache and Linux as the most robust platforms for running WordPress, but …
any server that supports PHP and MySQL will do. If your host doesn’t support the above, including mod_rewrite, you will probably be better off switching to another hosting provider, because there are a lot that do.
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Its going to be a tough road for you and your client, if you cannot interpret that enough to answer your own question.