you have two options,
create a log note for the related record with whom clicked while clicking the transfer button.
this is achieved with the feature of track_visibility
eg: partner_id = fields.Many2one('res.partner', string='Customer', track_visibility='onchange', index=True,
Here whenever you made change on the partner_id field will create a log note.
another value of track_visibility is 'always'
eg:
name = fields.Char(string='Task Title', track_visibility='always', required=True, index=True)
this will log values always has a data.
Lets take the first option.
make a new field which will update the flag when ever the transfer button clicks. and give the attribute track_visibility = 'onchange'.
eg: flag = fields.Boolean(string='string', default=False, track_visibility='onchange')
overide the function which trigger the transfer button and update the value. You can see the log note who is done the transfer.
or with the same function without the extra field you can create a log note for the record.