The short answer is yes, but how he gets them depends on which direction this case goes.
If this is a criminal matter, meaning someone reported the theft of federal pandemic funds, the FBI has jurisdiction. Stimulus checks are federal money, and stealing them is a federal crime. If an investigation is open, federal agents can subpoena email records directly from the provider. Your husband would not need to produce anything himself, the investigators would gather that evidence through their own process.
If your husband is pursuing this civilly, the path is through the discovery phase of a lawsuit. Once a civil case is filed, both sides have the legal right to request documents, communications, and records from each other and from third parties. Email records can be subpoenaed from providers like Google, Yahoo, or Microsoft with a court order. If the ex-wife sent emails admitting to what she did, those communications are potentially powerful evidence in that setting.
On the practical side, if your husband still has access to his own email account and those messages are sitting in his inbox or sent folder, he can simply download or screenshot them right now. Courts accept self-preserved email records, particularly when metadata includes timestamps and sender addresses. He should preserve everything he has before anything gets deleted.
The one thing worth knowing is that he cannot legally access her email account without authorization, even if he believes she used it to commit a crime. Any evidence gathered that way would likely be inadmissible and could create legal problems for him.
If this case has real merit, an attorney consultation is worth the time.