You do not have to allow this and as directors of the company the corporations act does not permit either of you to do anything that is to the detriment of the company.
Having said this if he does not want to work anymore all you can do is offer to buy him out of his share and there will have to be an agreement that he will not compete with you and not contact customers of the company.
If he refuses then you are in a stalemate and will have to have a court order as to what will happen.
Alternatively he keep it buy you out.
Because you do not have a shareholders agreement on what happens if you cannot reach an agreement the court will have to decide.
Here is a link sexting out the duties of directors to the company and other members
I am sorry I cannot give you a simple answer but the options you have are as stated but you both have to honour your duties under the law.
I hope this makes sense and is of assistance. if there is nothing further
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