I agree that the 555 circuit isn't drawn correctly.
The BD679 circuit also doesn't make sense. If there is a solenoid at its output with a low resistance, then the BD679 won't turn on.
Is the high-current pushbutton switch at the circuit's output and feeds the capacitor's charge into the solenoid? Then when the capacitor's voltage discharges low enough, the BD679 turns off the rectified input current from continuing to activate the solenoid.
Surely a fast-rising and fast-falling pulse from the 555 as a monostable timer driving a high-current Mosfet would work much better.