Doctor H sent up to 65 messages a day to Ms A's phone number, many followed by phone calls, some from his surgery landline.
The director of proceedings, Aaron Martin, said the idea of conducting an affair through someone else's phone was "implausible", and the suggestion that his lover's nickname was the same as his patient's abbreviated first name was "highly contrived".
There was no "reliable corroborating evidence" to prove their claims, Mr Martin said.
He described their evidence as "inconsistent", and at times "descending into farce".
"The volume, frequency and content of the messages amount to sexual transgression and impropriety," Mr Martin told the tribunal.
"Moreover, the content of the text messages is such that the tribunal can, on the balance of probabilities, infer that [doctor H] and [Ms A] were physically intimate."
The doctor had relied on a narrative that "lacks credibility", Mr Martin said, adding his behaviour had been "wholly unacceptable".
"The prosecution case is that [doctor H] took advantage of her situation and exploited it for sexual gratification, and that is a gross breach of trust in the doctor-patient relationship," he said.
However, both doctor H and Ms A gave evidence to the tribunal denying a sexual relationship, and corroborating the affair with Ms B, lawyer for the doctor, Harry Waalkens QC said in his closing statement.
"The unique situation of both the alleged recipient of the sexualised texts and the sender utterly rejecting the sexualised texts were intended for [Ms A] is compelling evidence," he said.
"Neither were shaken in cross examination on this point."
Doctor H admitted to having an "intense sexual relationship" with Ms B, and that he had been wrong to send messages to her via a patient's phone.
"It is accepted that [doctor H] has breached the appropriate standards of professional boundaries by sending the sexualised text messages for [Ms B] to her via [Ms A's] cellphone given she was a patient," Mr Waalkens said.
The doctor had expected all messages to be deleted immediately, as he did on his phone, and had been given assurances they were, Mr Waalkens said.
"He did not, however, engage in a sexually inappropriate [relationship] or transgression or violation with his patient, and the director of proceedings has not proved this aspect of the charge."
The tribunal reserved its decision, saying there was a lot of "complex material" for the panel members to examine before coming to its conclusion.
"We need to get to the right decision," panel chairman Bruce Corkill said. "We are going to be looking at this very carefully indeed."