1.) Currently when you create the invoice, system by default takes the current user ans salesmane in the invoice, so first of all remove that behaviour from the invoice.

'user_id': fields.many2one('res.users', 'Salesman', readonly=True, states={'draft':[('readonly',False)]}),
_defaults={'user_id':False}

2.) Now define an onchange_method for 'partner_id' field for fetching the salesperson from 'res.partner' model.

def onchange_partner_id(self,cr,uid,ids,partner_id,context=None):
    
    res={}
    obj_partner = self.pool.get('res.partner')
    if partner_id:
        br_partner = obj_partner.browse(cr,uid,partner_id,context=context)
        return {'value':{'user_id':br_partner.user_id.id}}
    return {'value':{}}

3.) Also if invoice is created from some other code (not from invoice screen), and you want forcefully the salesman to be related to the customer, then you need to override the create method of account.invoice model.

def create(self,cr,uid,vals,context=None):
    if vals:
        partner_id=vals.get('partner_id',False)
        if partner_id:
            obj_partner=self.pool.get('res.partner')
            br_partner = obj_partner.browse(cr,uid,partner_id,context=context)
            vals.update({'user_id':br_partner.user_id.id})

    return supser(<<your class name>>,self).create(cr,uid,vals,context=context)
                

Hope this helps !!