The problem here is that the two teams are not working together, but that the developers are supposed to reimplement the HTML. This slows the designers down and wastes the developer's time.
Instead, the teams should work closer together. In particular, the files that the designers create should be put into production with minimal changes. How can this be possible?
Use a template engine. Don't directly put PHP into HTML files, but use separate templates that are rendered by your PHP application. Give your designers a tool to test these templates, possibly an easy to deploy version of the application itself. Writing templates involves a tiny bit of programming, but it is mostly just about inserting the correct variable or maybe a few conditionals and loops. Templates are also great because the designers can insert a bit of presentational logic here, instead of having to negotiate this with developers.
PHP itself can be used as a template engine, but it is too powerful and has a potentially difficult to understand syntax. So the templates that the designers work on should be editable without having to understand PHP.