Hi,
Yes. First, you want to activate the "Payment of orders not paid immediately" setting in the HikaShop configuration so that orders can be paid on the frontend after they've been created, and not only during the checkout process.
Then, you want to go in the menu System>Order statuses and check that the order statuses are correctly configured. The payment of orders is only possible when the status of the order is equal to one of the enabled order statuses under the "unpaid" column there.
That way, if you access the listing of the orders as a customer on your frontend, you'll see an action button to pay the order if it's in the correct status.
Then, you need to know that when you change the status of an order in the backend and check the checkbox to notify the customer (or if you use the "email" button of the order edition page), if the order status of the order is enabled in the "unpaid" column of the System>Order statuses menu, then a payment link will be automatically added to the notification email so that the customer can just click on that link.
You can check the resulting emails in the Customers>Email history menu, and you can also use the "preview" button of the order stauts notification email via the menu System>Emails if you want to check how the email will look like.