"I immediately sent a text message in order to invite them."
Translation:Mi tuj tekstmesaĝis por inviti ilin.
I much prefer tuj over immediately (especially the spelling aspect) but I prefer IM over tekstmesaĝi. :/ (same reasons)
Or "I'll text you later" instead of "I'll send you a text message later".
I mentally do not think of a text as the same thing as an IM. Text is phone, and IM is computer, and IM feels as though it is dying out, though I still like the idea of it though I don't do as much of it as I might like.