Try select the invoices you would like to send and go to top menu click on "send invoices" as this should work as I am having the same problem here when when clicking on mail icon on the invoice list page under actions column. Or you may need to check your mail settings on Joomla Global Configuration section.

I'm having the same problem: "Could not instantiate mail function".
It's not happening with all e-mail addresses though. I checked the ones, where the problem showed up, the are all correct.
I also changed imn Joomla Configuration the E-Mail settings, no difference.

I am having this same problem. Joomla mailing is working perfectly, but Invoice Manager mail is giving the very same errors:

Notice: Could not instantiate mail function.
But it gives the below message at the same time though the mail never leaves the system.
Message: Invoice Inv-2015-06-17-1 sent to ajixxx@dxxx.com

PLEASE help us out.
@ari, were you able to sort it out?

Glad to say that @Germinal helped me out and its working great now. I was using a different email in the "From" field, from the one in the Global configuration, and the server default email. I had a xxx@daydah.com email there, while it was sitting on our daydah.net server so the server refused to send out the mail. Thanks to Joomlathat for the support!