Hi Alexander,
As Kevin stated above, you can use the Running balance option, which will give you the list of all invoices issued within your selected period. If this is what you were referring to in your question, then this is a perfectly suitable method.
However, if you wish for your customer to have full access to the invoices, including the ability to view and download them as PDF, then you should do the following:
Head over to Sales > Customers > All and open the desired contact. Click on the Email statement button, as per below:
This will send and email out to your customer, containing the link to view their full statement.
If you wish to preview the page they will be gaining access to, you can go to Sales > Customers > Contact and click on the Full statement button. You will be presented with the full statement, containing three URLs which can be shared with a customer. Click on the top link, as per below, takes you to the exact page your customer will be viewing, comprising all the Unpaid and Paid invoices and Quotes in a PDF form.
Should you want to change the number of the invoices displayed, click on Edit contact as indicated above, select Other information from the menu on the left hand side and edit Visible statement items.
I hope this clarifies your question.