At the moment when a person makes any false statement with the intent that it be believed by the other party, and that the liar benefit or the other party suffer harm because of this belief, the person has committed attempted fraud. If the lie is in fact believed, and harm does result, actual fraud has been committed.
Fraud is both a crime and a tort (private wrong). Often authorities choose to leave it to a civil suit by the victim rather than start a criminal prosecution. But that is a matter of policy or choice by the authorities, who may choose to prosecute any instance of fraud if they see fit.
Such a situation may involve other crimes as well. For example, in the US, if the false statement is transmitted electronically, it is probably wire fraud, 18 U.S. Code § 1343 - Fraud by wire, radio, or television provides that:
Whoever, having devised or intending to devise any scheme or artifice to defraud, or for obtaining money or property by means of false or fraudulent pretenses, representations, or promises, transmits or causes to be transmitted by means of wire, radio, or television communication in interstate or foreign commerce, any writings, signs, signals, pictures, or sounds for the purpose of executing such scheme or artifice, shall be fined under this title or imprisoned not more than 20 years, or both. If the violation occurs in relation to, or involving any benefit authorized, transported, transmitted, transferred, disbursed, or paid in connection with, a presidentially declared major disaster or emergency (as those terms are defined in section 102 of the Robert T. Stafford Disaster Relief and Emergency Assistance Act (42 U.S.C. 5122)), or affects a financial institution, such person shall be fined not more than $1,000,000 or imprisoned not more than 30 years, or both.
Under that law merely transmitting the false statement as part of a "scheme" breaks the law.