I had a little old lady show me how she put the deck belt back on.
She used a ratchet tie down, with the ratchet end hooked over the right footboard then run over the floor round the left foot board then down onto the tension pulley arm.
On the tension arm she said the hook kept popping off so she ran the strap around it and hooked the hook back over the strap.
Usually I slip a long wrench on the pulley nut and use that for extra leverage.
Run the belt over the tension pulley but leave it off the left pulley so when you pull the tension arm back it will be easy to slip the belt one and you are not working deep under the mower.