There is no way to pass any custom value directly from Sales Order to Picking. But, still there is a way to do that as follow:

1) There is a m2o field in "procurement.group" object called "sale_id" and we can use this field to fetch the data from Sales Order.

2) Override "_get_new_picking_values" method of the "stock.move" object and add a field of the picking to which you want to pass the value and fetch the value from the "self.group_id.sale_id.field_name"

Ex I want to pass some texts to note field of the picking:

Class StockMove(models.Model):
    _inherit = 'stock.move'

    def _get_new_picking_values(self):
        res = super(StockMove, self)._get_new_picking_values()
        # Pass value of note field from Sales Order to Picking
        res.update({'note': self.group_id.sale_id.note})
        return res