Glad I refreshed the screen - alba has posted a couple of the ones I was going to suggest you look at. Another that looks possible is Vassal - "Play live on the Internet or by email" - that needs more info which I'd guess is in the site somewhere -
http://www.vassalengine.org/
I *presume* you'd both need to download the engine & the Monopoly Module -
http://www.vassalengine.org/wiki/Module:Monopoly
Before doing that, I'd have a look in their Forum -
http://www.vassalengine.org/forum/
& see if any Q's you've got have already been answered.
Sorry, but I have *NO* experience of Vassal & hadn't heard of it until now, so can't comment on its suitability, ease of use or trustworthiness, although that last factor appears to be covered by online reviews as being positive.
One last thing - however you try this, I imagine the game is almost certainly going to be the US version, but whether any of them allow for modifying the board, I can't say.