InMail messages is a premium feature, and it allows you to directly message another LinkedIn member that you're not connected to. If you have a Basic (free) account, then you can only directly message LinkedIn members that you’re connected to. You must upgrade to a Premium account to use InMail messages. You may be able to send a follow-up or second InMail message to a LinkedIn member, even if they have not yet accepted or responded to your first message.
You’re allotted a specific number of InMail message credits based on your subscription type. You can find the number of InMail message credits you have from your My Premium page.
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