Increasingly, connected communication technologies have resulted in people being exposed to fraudulent communications by scammers and hackers attempting to gain access to computer systems for malicious purposes. Common influence techniques, such as mimicking authority figures or instilling a sense of urgency, are used to persuade people to respond to malevolent messages by, for example, accepting urgent updates. An ‘accept’ response to a malevolent influence message can result in severe negative consequences for the user and for others, including the organisations they work for. This paper undertakes exploratory research to examine individual differences in susceptibility to fraudulent computer messages when they masquerade as interruptions during a demanding memory recall primary task compared to when they are presented in a post-task phase. A mixed-methods approach was adopted to examine when and why people choose to accept or decline three types of interrupting computer update message (genuine, mimicked, and low authority) and the relative impact of such interruptions on performance of a serial recall memory primary task. Results suggest that fraudulent communications are more likely to be accepted by users when they interrupt a demanding memory-based primary task, that this relationship is impacted by the content of the fraudulent message, and that influence techniques used in fraudulent communications can over-ride authenticity cues when individuals decide to accept an update message. Implications for theories, such as the recently proposed Suspicion, Cognition and Automaticity Model and the Integrated Information Processing Model of Phishing Susceptibility, are discussed.