To fix the error message "the Installation of Tansee iPhone Message Transfer for Mac Failed", follow these steps:

Go to the Apple menu in the top left corner of your screen and select "System Preferences."

In the System Preferences window, click on "Security & Privacy."

Select the "General" tab.
Under the "Allow apps downloaded from" section, you may see different options. By default, macOS allows apps to be downloaded from the App Store and identified developers.
To allow the app to run, click on the lock icon at the bottom left corner and enter your administrator password if prompted.

Now, choose one of the following options:
If you want to allow apps downloaded from anywhere, select "App Store and identified developers."
If you want to restrict app downloads to only those from the App Store and identified developers, select "App Store." After selecting your preferred option, close the System Preferences window.
Try opening the app again. It should now run without displaying the error message.