iMessage from IMac to IPhone
hmmm… initially I thought this couldn't be done, however.

From messages, start a new conversation, from the top right icon. Start typing your own name until you can select your iMessage-capable account, accept then type the message.
Send.
A few seconds later the message will arrive on both devices &amp; you can then converse with 'yourself' - though it will all appear in both columns, as though you were actually talking to 'yourself'.

Looks odd - but it works.

Tested initiating on both iPhone &amp; Mac. Both work.

iPhone seems to generate multiple conversations for some reason, but the Mac keeps it inline.
Minor inconvenience, I'd say, for the benefits of being able to talk to yourself ;-)