It is possible to embed Minilessons in other parts of Moodle by using a Poodll / Generico widget to manage the embed.
Getting the The Minilesson ID
You will need the id of the Minilesson to embed. To get this visit the minilesson and check the URL as displayed in the browser address bar. You will see the "id" parameter on the URL. The value of that id parameter is the MiniLesson id.
Setting up the Poodll / Generico MiniLesson Embed template
You will need the Poodll or Generico filters installed on your Moodle site. In the admin settings for the filter plugin, there will be a "templates" page containing a list of existing and blank template settings pages. On a blank template settings page create a "MiniLesson Embed" template by choosing it from the presets if it is there. If it is not there, download the attached .txt file, and drag the file and drop it over the green bundle box on that template settings page. Then save the page. You have set up the MiniLesson Embed template. You only need to do this once. After that you can use it anywhere on your Moodle site.
Embedding the MiniLesson
If you also have either the Generico or Poodll toolbar icon installed for the Moodle HTML editor, you will be able to choose the "MiniLesson" Embed button, enter the MiniLesson ID and insert the filter tags into the HTML editor. If you don't its fairly simple to just type in the tag. (Copying and pasting can bring in invisible html characters that bust the processing, so it is better to type it out longhand.)
{POODLL:type="minilessonembed",width="800",minilessonid="540"}
or
{GENERICO:type="minilessonembed",width="800",minilessonid="540"}