If you have sent through a client invite but your client isn’t seeing the invitation on their home screen to accept it then there is a high chance they are signed up as a partner themselves. Partners are unable to connect with other partner accounts.
A lot of the time the client is not aware that they have signed up as a partner but one of the obvious sign is if the account owner has the Partner Menu icon in their account.
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For them to deactivate their account as a partner they can click this link while they are logged into their account - https://go.servicem8.com/help_me/DeactivatePartnerAddon
Once they are no longer a partner they should be able to view your invite.