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Yes you can use pagination=”yes” attribute for pagination.
Example: [show_posts_pbs_rk layout="1" no_of_post="6"  pagination="yes"]

in the above shortcode number of post is set to 6 and pagination is set to yes. So if number of post will greater than 6 then pagination will appear.

Okay, pagination will not work if category_id attribute in shortcode.
If you want to use pagination then you have to remove category_id attribute from shortcode.
Currently pagination will work with all attribute except category_id.
Thank you.

I have created a quick code for you.
You can paste this code above return $content; in posts-by-shortcode-rk.php file.

/* Show Pagination for category attribute */
	if($pagination_attr == 'yes' && $category_id != 0){
		
		$args = array(
		  'cat' => $category_id,
		  'post_type' => 'post'
		);
		
		$the_query = new WP_Query( $args );
		$total_posts = $the_query->found_posts;
		$total_page = ceil($total_posts/$post_per_page);
		
		if($total_posts > $post_per_page){
			$content .= '<div class="pbs_rk_pagination">';
			$content .= '<ul>';
			
			for($count = 1;$count<=$total_page;$count++){
				if($_GET['offset'] == $count || (empty($_GET['offset']) && $count == 1)){
					$content .='<li class="active"><a href="?offset='.$count.'">'.$count.'</a></li>';
				}else{
					$content .='<li class=""><a href="?offset='.$count.'">'.$count.'</a></li>';
				}
			}
			
			$content .= '</ul>';
			$content .= '</div>';
		}
	}

I hope it will help.

I have added new version of plugin and added functionality of pagination to category_id attribute.
I have added more attribute to shortcode for more control. you can use them now.