So the image is presented through the img srcset
so in theory, and this will not work, you would need to add an anchor tag around the img specifically and call the sources via a srcset:
<picture>
<source srcset="1380.jpg"media="(min-width: 1380px)">
<source srcset="990.jpg"media="(min-width: 990px)">
<source srcset="640.jpg"media="(min-width: 640px)">
<a srcset="320.jpg"">
<img srcset="320.jpg">
</a>
</picture>
But this above will not work as HTML alone.
You could do something like this:
<a href="newpage.html">
<picture>
<source srcset="https://placeholdit.imgix.net/~text?txtsize=33&txt=1380%C3%97150&w=1380&h=150" media="(min-width: 1380px)">
<source srcset="https://placeholdit.imgix.net/~text?txtsize=33&txt=900%C3%97150&w=900&h=150" media="(min-width: 990px)">
<source srcset="https://placeholdit.imgix.net/~text?txtsize=33&txt=650%C3%97150&w=650&h=150" media="(min-width: 640px)">
<img srcset="https://placeholdit.imgix.net/~text?txtsize=33&txt=350%C3%97150&w=350&h=150">
</picture>
</a>
Then on the new page:
<html>
<head>
<meta name="viewport" content="width=device-width; height=device-height;">
<style>
</style>
<title></title>
</head>
<body>
<picture>
<source srcset="https://placeholdit.imgix.net/~text?txtsize=33&txt=1380%C3%97150&w=1380&h=150" media="(min-width: 1380px)">
<source srcset="https://placeholdit.imgix.net/~text?txtsize=33&txt=900%C3%97150&w=900&h=150" media="(min-width: 990px)">
<source srcset="https://placeholdit.imgix.net/~text?txtsize=33&txt=650%C3%97150&w=650&h=150" media="(min-width: 640px)">
<img srcset="https://placeholdit.imgix.net/~text?txtsize=33&txt=350%C3%97150&w=350&h=150">
</picture>
</body>
</html>