From the Guidelines

There is no conclusive evidence to suggest that anesthesia and morphine have a long-term effect on Alzheimer's disease.

The current evidence does not support a direct causal link between anesthesia, morphine, and the development or progression of Alzheimer's disease 1.
Research on postoperative cognitive dysfunction (POCD) has shown that cognitive decline can occur after anesthesia and surgery, but the natural history of these changes is not well understood, and causal associations remain unclear 1.
Opioids, including morphine, have been shown to have side effects such as postoperative ileus, urinary retention, nausea and vomiting, shivering, and opioid-induced ventilatory impairment (OIVI), but their long-term effects on cognitive function are not well established 1.
Preclinical studies have demonstrated neuroanatomical changes and lifelong cognitive deficits after exposure to common anesthetics in early life, but these findings have not been consistently replicated in human studies 1.
Delirium, a common complication of anesthesia and surgery, has been linked to subsequent cognitive decline, but the relationship between delirium and Alzheimer's disease is complex and not fully understood 1.

Clinicians should be aware of the potential risks and benefits of anesthesia and opioid use in patients with Alzheimer's disease or those at risk of developing the disease.
Further research is needed to fully understand the relationship between anesthesia, morphine, and Alzheimer's disease, and to develop evidence-based guidelines for the management of patients with Alzheimer's disease undergoing surgery or receiving opioid therapy.

The FDA Drug Labels for morphine (PO) do not address this question.

From the Research

The available evidence suggests a possible association between general anesthetic exposure and the onset and progression of Alzheimer's disease (AD) 2, 3, 4, 5, 6.
Studies have shown that postoperative cognitive decline in the elderly has emerged as a major health concern, and there is a growing interest in the potential relationship between general anesthetic exposure and the onset and progression of AD 2, 3, 4.
A growing body of evidence suggests that general anesthetics may be neurotoxic to both young and aging brains, with much of the evidence originating from in vitro and in vivo studies with cells, rodents, and nonhuman primates 2, 6.
However, despite the animal data suggesting a relationship between anesthesia and neurotoxicity in the elderly, a definitive link remains elusive in humans 2, 5.

There is no direct evidence in the provided studies to suggest a long-term effect of morphine (opioid analgesic) on Alzheimer's disease.
The studies primarily focus on the relationship between anesthesia and Alzheimer's disease, with no mention of morphine or opioid analgesics as a potential factor 2, 3, 4, 5, 6.

The possible relationship between anesthetic agents, cognitive dysfunction, and Alzheimer disease remains to be clarified, and prospective cohort studies or randomized clinical trials are required for a better understanding of this association 5.
Further studies are needed to address the link between exposure to general anesthesia and the development of AD in humans, and to determine the potential risks and take cautions with vulnerable elderly patients 6.