I have never tried this transition from the player side, but I have done it once as a GM.
The first thing, is to make sure there is interest. If most of the other players are not interested in play by post, then it is probably best to move on or start a "spin-off" with those that are.
If you know there is interest, then you need to get consensus on how things will change. There are all kinds of play by post styles available, but for me I find running traditional combat very slow and boring in that situation. Instead I look at options like letting the gm make more of a summary style where combat is handled in just a few posts mostly by the gm, or even a sim-style where there is no rolling or dice at all and everything is by consensus. There are other options and some people do run close to traditonal style combat with turns and dice rolling, but I find it painfully slow. Regardless of which method you choose you will need to get buy in from the gm and other players on what method you will adopt.
Finally, the best way to keep interst strong and encourage others is do the hard work. Of course a game can continue with nothing but a forum (or e-mail mailing list, which I prefer personally) and setting up a forum (or list) is fast and easy. But if you want to encourage less-than-enthusiastic players you can do some of the nice, but not strictly necessary work, like:
- Create a page with a summary of what has happened so far.
- If appropriate for your game, create sub-forums for things like out of character chatting.
- Create a summary every so often (monthly is good, but depends on your speed of play) to help people get caught up.
- Depending on the game and group, it might help to have someplace to post character sheets, character pictures, and maps.
If you get player buy in, work out the details, and then do the hard work to get things set up, then there is a good chance that the others will go along with it. But it is also possible you can do everythign right and still have things fall apart if the other members of your group do not like play-by-post/PBEM.