The image shows two messages reportedly by the politicians, with Cummings criticising how the UK Health Minister Matt Hancock handled the mass Covid-19 testing programme during the onset of the pandemic in Britain.
Cummings shared another post on his Twitter page on Wednesday, suggesting that the PM should answer a "few simple questions."
When he appeared before Parliament's health and social care and the science and technology select committees on 26 May, Cummings made serious allegations against Hancock among other controversial revelations about Downing Street as a whole.
Cummings had said Hancock should have been fired for repeated mistakes and "lying to everybody in multiple occasions in meeting after meeting in the cabinet room and publicly".
According to Cummings, Hancock had claimed that all patients got the treatment they needed during the first peak of of the pandemic but in fact it wasn't true. Hancock told officials that the supply of personal protective equipment was under control in April 2020, which later turned out to be not true, Cummings had told the MPs.
When asked during the inquiry whether he will be able to provide evidence to support his statements, Cummings agreed to present it to the committees. Three weeks later he shared the exchange between him and Johnson for the whole world to see.
Another apparent exchange between the PM and his former aide, showed that Johnson wanted to give Minister for the Cabinet Office Michael Gove - as opposed to Matt Hancock - responsibility of PPE during Covid crisis.
The PM reportedly told Cummings that the PPE situation was “a disaster”.
Cummings disagreed with replacing Hancock because “With the [Cabinet Office] in such a total s***show i’m afraid we’d have a severe risk of making things worse not better.” He added that "the government does not control the government” but the Cabinet Office “controls most of it”.
“Hancock b*******s but that wouldn’t matter much if we actually controlled the [Cabinet Office]," Cummings wrote to the PM.
A spokesperson for Boris Johnson said on Wednesday that the PM doesn't plan to engage with every allegation made and that the government’s focus is on delivering for the public. The PM has full confidence in Matt Hancock, said the spokesperson, dismissing rumours of Johnson stepping down early.
Cummings was sacked as Prime Minister Boris Johnson's special adviser in November last year, in what later was reported to be a controversial end to their relationship.