LinkedIn Recruiter and LinkedIn Recruiter Lite don't have a draft feature for InMail, but you can save the message as a template and send it later.
You can access and manage your templates from the Inbox at any time:
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Click the Messages icon at the top of your Recruiter or Recruiter Lite homepage.
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Click the
Settings icon at the bottom left of the message list on the left rail. -
Select Message templates.
The Message Templates page displays all templates you created or have been shared with you.
(Recruiter only) If an admin on your contract turns off automated follow-up messages, all associated templates, including 2-message templates, won't display under Product settings or while composing a message.