My read on your question suggests to me that you could start at the basic level with raw HTML. Let's stay platform agnostic in your workflow.
- Get a text editor that promotes its ability to work in raw HTML.
- Review an on-line tutorial that instructs how to work with the beginning elements in raw HTML.
The most basic format will have HEADER and PARAGRAPH elements as its only input. You may eventually include LIST elements. HEADERS would include such things as Education, Experience, Publications, Proposals, and Professional Affiliations. PARAGRAPHS and LIST elements would be under these headers. All the effort at this stage is simply to copy + paste the current information into the new HTML.
Once the basic HTML works and has all the content required, move to formatting. The standard approach for this is to incorporate a CSS style header or CSS style file. Will you need lots of CSS styling commands? Not really. Define the text size and font face in each ELEMENT (HEADER, LIST, PARAGRAPH). One distinct advantage with HTML (over PDF) in this case is the ability to use relative font sizes, allowing the person viewing the page to scale for their own needs. One certain reason also to include a basic CSS is to define the view for different platforms such as desktop versus tablet versus mobile device.
Can this process be automated? Perhaps. But ... for what you are asking ... the time you would invest to find, set up, and establish proficiency with an automated tool is likely not minimal. Alternatively said, you can probably find a good application that will allow you to do WYSIWYG layout designs of Webpages, but it will likely over clutter the source with its own ELEMENTS (e.g. SPAN, DIV, ID), perhaps include additional page settings (e.g. width=...), and maybe even end up putting in javascript code. By implication in you posting, you are seeking to avoid this. Also alternatively said, you may find a tool that will allow you to take the current input, run it through a filter, and have it automatically produce a new HTML to a different format. Then you will likely have to learn how to design your desired filter for old -> FILTER -> new.
You may struggle with raw HTML editing to achieve elegance in the Webpage design. Be prepared at that point to need additional CSS ELEMENTS. Rather than learn how to do this with raw HTML on your own, consider two options. Find a professionally designed template that provides what you want. Copy and paste the content from the old CV to the template. Otherwise find a WYSIWYG Web page design application, layout the content in the format that you want, push a button, and get a Webpage. The advantage is that you can format in almost any way you want.
As to adding content dynamically to HTML, the only way to do this is using a server-side script method. One example is to allow your friend to keep a CSV file for publications, download that file to the Web server, and have the Web CV automatically update with the most recent list. This avoids the need for anyone to have to re-edit the raw HTML later, e.g. simply to add a new publication to a list. This step could be a later investment in your effort, but only when you have confirmed that the server can support server-side delivery of scripts.
In summary, an automated tool to convert from an existing format to a new format may not exist or simply be too much work. Doing raw HTML coding is the most future-proof approach. It may however not provide you with an end result that you consider to be the most elegant. If so, consider copying into a template or using a WYSIWYG application. Finally, assure yourself that someone else (e.g. especially the owner of the CV) will be able to reproduce the approach that you take to put content together with format, especially if you will not be responsible to update content later.