How to replace all "http" hyperlink with "https" in my wordpress posts

If your host provides you with phpMyAdmin or some other user interface to run MySQL queries, you can do this pretty easily with a MySQL query. For example, you would run the following query on an SQL tab in phpMyAdmin:
UPDATE wp_posts SET post_content = REPLACE(post_content, 'http://yourdomain', 'https://yourdomain')
You’ll have to substitute the “wp_” with whatever prefix you’re using for your WordPress tables if it’s not “wp_.”

The important thing is to include your domain name in the from and to strings in the MySQL REPLACE function so that only the protocol for your domain is changed, not the protocol for links to other sites that may not have SSL.

Of course, make sure you back up your database, or at least the wp_posts table before you do this unless you’re feeling very confident.

You’ll also need to go through your Widgets manually to change the protocol there, or you can use relative URLs.