Or, he could create a VPN link, but this would be even slower for browsing.
With RemoteDesktop (RD), or VNC for that matter, they would control your computer, so browsing would be done at your speed. However, the data on your computer would only be sent to them as fast as their dial-up would allow.
If you set up a VPN, then the default is for internet data to go through the VPN tunnel to your network, then use your gateway to access the internet. This would mean that if they did a TRACERT to any website, you would see it going from them, to you, then out - and is likely to crash out due to the latency involved. This often happens even when using broadband internet at both ends, so it will be worse using dial-up.....
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I've seen the light... It was green, flashy and attached to a Network Interface Card...
Whenever someone says "You can't miss it" I invariably do...