1. A biometric authentication device that performs biometric authentication based on biometric information input to a connected terminal device, the biometric authentication device comprising: a storage device configured to store a first enrolled template and first information including a parameter representing a type of a first input sensor to which the first enrolled template was input; a receiver configured to receive biometric information transmitted from the terminal device, a second enrolled template stored in the terminal device, and second information including a parameter representing a type of a second input sensor to which the second enrolled template was input; and a processor configured to execute a process comprising: performing authentication of a person who inputs the biometric information by matching the received biometric information and the first enrolled template; calculating a judgement value φ according to a formula below in which Wc indicates a weighting value of the second enrolled template, Sc_c indicates a similarity between the received biometric information and the second enrolled template, Ws indicates a weighting value of the first enrolled template, Sc_s indicates a similarity between the received biometric information and the first enrolled template, and A indicates an adjustment parameter; 
 φ= Wc×Sc _ c−Ws×Sc _ s+A selecting the first enrolled template or the second enrolled template based on the first information, the second information, and the judgement value φ; and replacing the first enrolled template stored in the storage device with the second enrolled template that is received by the receiver from the terminal device when the second enrolled template is selected, wherein when the received biometric information is accepted in the authentication, and when the type of the first input sensor and the type of the second input sensor are different from each other, and when the judgement value φ is larger than or equal to zero, the processor selects the second enrolled template and replaces the first enrolled template stored in the storage device with the second enrolled template.