Hi Guillermo,
First, do not place or run canonical tags from your site to the amazon like site. This would be telling Google that their site is in fact the authority source for the products which are for sale. Doing this in the long run would untimately kill your clients web traffic and site in time.
Next, look at both your site and amazon-like product site. Is it pulling in the product descriptions dynamically or do you have to update them manually between both sites (your client and the amazon site)? This is an important step when trying to strategize how to best implement the tactics you will use.
Next, look at the client site. If you really want to build this site up, it's going to take some work. Here are a few things you can do to improve the client site information and
1. Write ALL NEW content descriptions about each product (this can take time, but it's worth every second). Make them fun and detailed providing unique approaches to the products being sold.
2. If you can, provide video reviews of the products, or use video to showcase the product in a way that will help people searching and researching it. Don't let this slide. It can also help your 'time on site' and time on page metrics which we know improve the overall success of a site online within the SERP results (Google).
3. Provide numerous images of the product. Realign this with improving the gallery function of the site to showcase products. Use at least 5-6 images per product from numerous angles and allow for clear visibility of the product. Make sure to offer both small thumbnails and when clicked on - clear large images that users can see. This again will help with product showcase.
4. Implement a feed which will allow users and visitors to comment on products (after purchase), thus offering some user feedback to visitors about each one sold, experiences, etc. This also helps improve sales conversion ratios and can also help the company identify trouble areas that need attention (customer service, shipping, the product itself, sales funnel and process, etc). If monitored, these can be invaluable info to help improve conversions and increase ROI.
5. Offer a blog on the site which reviews products to start. Use this tool to promote various products and offer in depth information about them. You can then move to develop a content strategy to improve the long tail search. Look to find keywords that revolve around clients 'searching' for the product using questions. Use these questions to develop content which provide answers. This is a key element now in search and should be leveraged to the best of your ability.
6. Implement a full social media strategy for the client site. Line up all the social media accounts to accurately reflect each other and unify them in the way they look and feel (descriptions, picture, info, phone #'s, etc). Make it all uniform. Next ensure you have the key elements and pages ready (LinkedIn, Facebook, Twitter, Google+, Pinterest). Line these up so that the client can use these to not only promote their products, content, etc, but to improve brand development and especially customer service. These platforms can be leveraged to so much more now than just 'sharing' good content and the client needs to understand this. Embed all these through social media 'share' buttons on each product page to improve the 'sharability' of these products online.
7. Research both the local and global search markets and align yourself with building each profile out (store location, local search, etc) Work to build and drive traffic on both levels using all the strategy.
8. Run A/B tests on the pages once all this is done. Look at your analytics data to identify things that need improvement. Funnel, descriptions, pages, added video, user feedback and reviews, etc. It will all help provide the depth you need to surpass the amazon-like site
Ultimately, work to make the pages unique in every way. See what this amazon site is NOT doing and work to improve the user experience.
Also - (but you should already know this
ensure that each page has clear and concise meta data, product descriptions, titles, image ALT tags, etc. This will also require some work, but is very key move. Not only will adjusting the content on the page
Taking the time to develop out a strategy like this, in the long run, will help improve the user experience by offering a superior site, customer services and sales!
Cheers!