As an editor of a publication on Medium, you can request published stories to be added to your publication.
Navigate to that story's page, which will look something like this:
Click on the icon with the three dots ("...") in the lower right corner under the story. A drop-down menu will appear with additional options:
Click on "Request story." You'll have the chance to select which publication you'd like to include this story in:
Click on the publication title.
Your Request
A screen will appear, reading: "Request this story for your publication":
The text box will contain a template message which you can use to request the story. You can edit this message, if need be, or click on "Send email" when you are ready.
Note: If you have entered an email address in your publication info, it will become the reply-to address when you request a story. If you do not add one, the reply-to address will be "noreply@medium.com."
If the author of that story has chosen to receive emails (this may be turned on or off from the settings page), they will receive your message and request by email.
They Will See...
The author of the story you requested will receive a note that includes both your message and some instructions:
The instructions explain that once an author submits their story to a publication, the editors will be able to include it in their publication, as well as edit it (authors will not receive notifications of edits) and be able to see any notes left on the story.
Story authors can refuse requests as they see fit. And if they've submitted a story to a publication and changed their mind, they may remove it at any time.
Submitted Stories
After a story has been submitted, that story will have a note at the top saying "Submitted to" and the name of the publication:
Managing Submissions
After a story has been submitted by the original author, the editor of the requesting publication will receive a notification:
By clicking on the submitted story, the editor will have a chance to review and make edits to the story.
To publish the story, an editor must click on the "Edit" button at the top of the story's page:
Then you must click through the "Publish" dialog:
Alternatively, once you've clicked "Edit" on the submitted story, you can also click on the "..." button next to "Publish" and then click on "Manage submission":
From the menu which appears, click on "Accept into publication":
The story has been added to the publication, but you still have to click through the publish dialog, as above.
The story status at the top of the story will be changed from "Submitted to ____" to "Published in" and the publication name:
Note: When a story is accepted into a publication, the author of that story is automatically added to the list of allowed writers for that publication. This means they will be able to submit additional pieces to the publication in the future.