First of all, it is necessary to find out whether this problem affects only one client (a few clients) or all clients. If the latter is the case, the problem is likely to be caused by incorrect global settings. If the former is the case, the problem may be caused by an incorrect individual setting in the Client card.
If invoices are not sent to any clients, check the proforma_automatic_send item in Invoicing / Settings / General. Using this item, you can globally set up the automatic sending of invoices after proforma invoice settlement. If the 0 (Do not send) option is selected, no invoice sending can happen.
It is not the only global setting that plays a role here. Even if you enabled the automatic sending of invoices after proforma invoice settlement (options 1-3), it does not necessarily mean that invoices will be sent.
Next, you can check the template settings. In Settings / Other / Email templates, a particular template must be chosen in the Default column. If no template is chosen, no emails with invoices can be sent.
If invoices are not sent to one particular client, check the relevant individual settings in the Client card: Is an email address entered in the form? Is the Send invoices via email checkbox checked? Is the Do not send invoices created from proforma invoices checkbox checked? If the Do not send invoices created from proforma invoices checkbox is checked, then no such invoices can be sent to the client.