This seems to be based on the assumption that if you prevent a malaria patient from having to go to the hospital, then that frees up resources for them to focus on saving a COVID-19 patient.
So if we were to oversimplify this as an example:
Let's say a hospital has 50 beds. There are 50 COVID patients and 50 malaria patients. Thus, you can only save half of them. If we were able to prevent malaria in those 50 patients, then the hospital can allocate all 50 beds to the 50 COVID patients - thus, saving everyone.
Now, I'm very sure there's much more to consider than my oversimplification - so I would love to hear people's thoughts and be proven wrong!
EDIT: I reached out to AMF for further clarification and here is their response.
There are several ways in which reducing malaria – both morbidity and mortality – helps reduce the impact of COVID-19.
First, if people are ill with malaria their immune system is less able to cope with the effect of COVID-19 so the impact of COVID-19 can be expected to be greater. This is consistent with those most at risk being people with ‘underlying health issues’. Increased malaria leads to a greater strain on already fragile health systems including taking up more intensive care beds.
Second, if people are ill will malaria, whose symptoms are very similar to those of COVID (high fever), (“….the early symptoms of COVID-19, including fever, myalgia, and fatigue, might be confused with malaria and lead to challenges in early clinical diagnosis.” Source: Lancet article) the identification and management of COVID-19 is made more difficult. There is a greater risk of mis/under-diagnosis (treated as malaria when in fact COVID-19) or over-diagnosis (treated as COVID-19 and perhaps a bed in a hospital allocated, when malaria is the illness), which makes the management of COVID-19 more challenging.
Third, if we delay desperately needed universal net coverage campaigns, and bednets are the most effective mechanism of preventing malaria, as well as other malaria control interventions, there is a significant risk, indeed a likelihood, that malaria will increase leading to further loss of life, illness, a greater strain on health systems trying to deal with COVID-19 as well as increased negative economic impact - if people are ill, they cannot farm, drive, teach, function.
For these reasons and as the WHO advises, it is important that malaria control activities continue. These activities are likely to require sensible operational adjustments, including increased sanitizing measures and social distancing, to limit transmission risk.