In one way your therapist is right, your boyfriend can gamble regardless of what you say but the method is not reducing harm – it is feeding his addiction.
I also have no belief that this method can help him in the slightest. Unless he accepts his addiction and seeks treatment it will get worse, never better.
Is your boyfriend saying he does want to control his gambling because it would appear he doesn’t want to do so? Some gamblers do not want to stop gambling and will not stop until they have hurt themselves enough and/or all enablement has ceased. It takes courage to control an addiction but I wouldn’t be here if it was not possible.
Giving cash to a gambling addict, whether it is $1 or a $1,000,000 is enabling his addiction. Maybe you could ask him how he wants you to help him because at the moment, he is asking you to keep his addiction alive and growing and it is hurting you to do so.
Please speak bluntly at you therapy session tomorrow, your boyfriend needs the right support and more importantly, as far as I am concerned, so do you. You are being brought down by his addiction and it will take you all the way down with it, if you allow it to do so.
I hope you are keeping your own finances safe, unfortunately it is harder to keep your heart safe and I understand that.
While your boyfriend is only prepared, in his life, to put himself first, please put yourself first, in yours Sunflower. If you lose your health and happiness then the addiction has claimed an extra life.