Thanks for your inquiry.
Aspose' products are used to programmatically generate, load, work with and convert many different document formats. These components are avaliable in .NET and Java platform. We do not offer any web service to submit documents for conversions.
Your client can however setup there own service on their server using Aspose components they can set up such a service on a server to handle conversion between file formats.
You could achieve what you looking for by using either Aspose.Words or Aspose.Pdf.
Using Aspose.Words you can load the HTML content from a webpage using the code of the second example from this API page here. You can then convert this to PDF and send to the users web browser by calling the Save method overloaded described here. Simply outputting the file name with ".pdf" will convert the HTML to PDF.
Using Aspose.Pdf you can insert HTML and convert it to PDF in a similar way which is described here.
If you have any further questions, please feel free to ask.