Small Engines (Lawn Mowers, etc.): Solenoid replacement, spade terminal, lawn chief

Question
I have a Lawn Chief 455-N mower that needs a new solenoid.  The solenoid taken out of it is an MTD 725-3001.  The issue is that the 14 hp  (14.5 hp) Kohler engine was swapped out for a 12.5 hp B&S engine.  The Briggs engine # is 789707-012101-81 and the solenoid for that is a 691656

If I put the Briggs Solenoid in I am concerned the wiring hookups will not be correct for the mower. As the MTD solenoid worked for the two years I have had it, I am tempted to go with that again.

Suggestions?

Thank you

Answer
The MTD has one small terminal, correct?  

If the Briggs solenoid only has one small terminal then it will work as both solenoids much ground through the mounting plate.

You may have to change the small wire connection, the exciter wire, as one may be an O/eye terminal and the Briggs is a spade terminal.
Let me know if this helps.

Eric