Philosophers say things like: "Asserting 'There is no conclusive proof that Smith is a plagiarist' implicates that there is a genuine possibility of Smith's being a plagiarist." (And yet taken literally "There is no conclusive proof that Smith is a plagiarist" is true even if no one ever suspected Smith of plagiarism.) However what one implicates not only has propositional content, but also illocutionary force, and both both the content and the force are implicated. So if we want to be more explicit, we should say something like: "Asserting 'There is no conclusive proof that Smith is a plagiarist' implicates the suggestion (or insinuation or even assertion) that there is a genuine possibility of Smith's being a plagiarist." Which of the forces--suggestion, insinuation or assertion--is the right one to choose is going to be a hard question to determine. Maybe there is vagueness (ugh!) here. In any case, we don't just implicate propositions--we implicate whole speech acts. A question can implicate an assertion and an assertion a question ("It would be really nice if you would tell me whether...").
I used to wonder whether the moral rules governing lying (which I think are very simple, namely that it is always wrong to lie, but I won't be assuming that) extend to false implicature. I now realize that the question is somewhat ill-formed. The moral rules governing lying are tied specifically to assertions, not to requests or commands. One can implicate an assertion, but one can also implicate other kinds of speech acts, and it only makes sense to ask whether the moral rules governing lying extend to false implicature when what is implicated is an assertion or assertion-like.
And I now think there is a very simple answer to the question. The moral rules governing lying do directly extend to implicated assertions. But just as these moral rules do not directly extend to other assertion-like explicit speech acts, such as musing, so too they do not directly extend to other assertion-like implicated speech acts, such as suggesting. The rules governing an implicated suggestion are different from the rules governing an explicit assertion not because the implicated suggestion is implicated, but because the implicate suggestion is a suggestion. If it were an explicit suggestion, it would be governed by the same rules.
That said, there are certain speech acts which are more commonly implicated than made explicitly--suggestion is an example--and there may even be speech acts, like insinuation (Jon Kvanvig has impressed on me the problematic nature of "I insinuate that...") that don't get to be performed explicitly (though I don't know that they can't be; even "I insinuate that..." might turn out to be a very subtle kind of insinuation in some weird context).
I think the distinction between the explicit speech act and the implicated speech act does not mark a real joint in nature. The real joint in nature is not between, say, explicit and implicated assertion, but between, say, assertion and suggestion (regardless of which, if any, is explicit or implicated). Fundamental philosophy of communication does not, I think, need the distinction between the explicit speech act and the implicated speech act. That distinction is for the linguists--it concerns the mechanics of communication (just as the distinction between written and spoken English, or between French and German) rather than its fundamental nature.