Modify WordPress to use header and top menu from external page with its own database

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Job Description

I have an online store (Prestashop) installed on my server. I also have a WordPress blog setup on the same server, in a subfolder.

The goal is to use the Prestashop header and top menu for both sites, so the user has easy access to store products and categories.

If the user can make the menu fixed that's something we might also be interested in implementing.

Samples of previous work, demonstrating skill in the field will be required.