Beal, a primary schoolteacher, had been accused of tying up Billingham and stabbing him to death "in cold blood" before burying his body in their Northampton garden.
She had previously pleaded guilty to manslaughter by reason of a loss of control but had denied murdering Billingham between 30 October and 10 November 2021.
After changing her plea partway through the trial, she will be sentenced next month.
Beal was arrested in March 2022 after police discovered the body and her actions were uncovered by the police through entries in her diary.
The prosecutor Hugh Davies KC told jurors that Beal, described as "a high-functioning professional", had messaged several people on 1 November 2021 to say she and her partner had contracted Covid-19 and were isolating at home. There was no evidence Beal had taken a Covid test, the prosecution said.
Similar messages were sent from Billingham's phone on 2 November, which was alleged to be Beal "pretending to be him" in a move that was "as heartless as it was self-serving".
Beal then told friends and family that she and Billingham had split up, with one message saying he had left her because he was having an affair with another woman.
The prosecution said this was "completely false", though Billingham had appeared to have cheated on Beal previously.
Beal returned to work as a year 6 teacher and was able to "fully discharge her considerable responsibilities" before her mental state deteriorated in February 2022, the court heard.
In March that year she rented a cabin in Cumbria and sent concerning messages to family members that prompted them to call the police to check on her, the prosecutor said.
In the cabin, police found journals "written in her hand" that contained "some unambiguo...