Wireshark is a program that monitors network packets moving across a network. It is free and popular. The final way to answer this question is to get Wireshark, take a day to learn it, and apply it.
The filter for viewing traffic from the source site will look like this:
(ip.src == [source ip address]) && & (ip.dst == [target ip address])
Change ip.src and ip.dst to find out what happens. In fact, you could combine both in one filter expression.
This will work as long as you are on the network through which the packages are distributed.
One last point: here is the PKI description (https / SSL / TLS): http://www.mitre.org/news/the_edge/february_01/steve.html
I wiresharked a similar situation, and confirmed that I send and receive TLS traffic (https). But this was not such a situation, so I do not want to speculate.
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