In which of the following scenarios would a process server be legally allowed to continue with their service attempt?

A process server is legally allowed to continue with their service attempt when they have a valid court order and the appointment is present. This is the correct scenario as the law recognizes the authority of a process server to execute their duties when they are acting within the parameters set by a court, which includes having a valid court document to serve. This validates their actions and gives them the legal backing necessary to proceed with serving papers.

In this context, the presence of the appointment ensures that the server is attempting to fulfill their obligation under legitimate circumstances, adhering to the legal requirements that govern process serving. This means that they are acting on behalf of the court and ensuring that due process is followed, which is critical in legal proceedings.

The other scenarios do not provide the necessary legal framework for a server to continue with their service attempt. For instance, simply asking kindly or being a law enforcement officer does not inherently grant the authority to serve documents without following proper legal protocols. Similarly, the absence of the subject does not prevent the server from attempting service, but without a valid court order, the server would be operating outside their legal authority.