Welcome to the Forum. We have an "Introductions" area, also.
You have not given us enough information about your firearm. Does the barrel indicate what caliber it is? If it was designed for the 44-40, then no.
With few exceptions, do not use ammo in a firearm that it was not designed for.
"A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed."
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Life Member NAHC