The £67bn ($108bn) is 3.2% higher than the previous bid and 14% higher than its initial offer last month.
It is the third time that InBev has made a higher bid for the company, with previous offers at £38, £40 and £42.15 per share.
Shares in SABMiller closed flat at £36.67 in London following the latest bid, valuing the company at £60.2bn.
SABMiller has rejected the previous offers, claiming that they "very substantially" undervalued the company.
InBev has accused SABMiller's board of being unwilling to enter talks about a deal.
Last week Carlos Brito, chief executive of InBev, said its proposal "creates significant value for everybody. How long will it be before shareholders see a value of over £42 in the absence of an offer from AB InBev?"
Under UK takeover rules, InBev has until 16:00 GMT on Wednesday to make a formal bid for the maker of brands including Peroni and Grolsch or walk away for six months.
InBev brews beers such as Budweiser, Stella Artois and Corona among others.
If a deal is struck, it would create the world's biggest brewer and be the UK's biggest corporate takeover.
SAB has several large shareholders, which have so far sided with the London-listed company and said the offers undervalue it.
South Africa's Public Investment Corporation, the fourth-largest shareholder in SAB, said on Friday that the price was too low.
A deal will not succeed without the support of tobacco company Altria, which has a 27% holding, and Colombia's Santo Domingo family, which owns 14% of the shares.
SABMiller tried but failed to acquire Dutch rival Heineken a year ago.
Anheuser-Busch InBev has increased its offer for rival brewer SABMiller to £43.50 a share.