Technically, a registered business (whether sole proprietorship or a partnership) cannot be converted to a company. A registered business (that is, a sole proprietorship or a partnership) is a separate legal entity from a company and the law does not provide any process for conversion. Instead, what needs to be done is to terminate the registered business (that is, the sole proprietorship or partnership), inform ACRA that you have ceased to carry on business as a registered business and incorporate a new company. 
Then you may need 
(i) to transfer the business assets that will be used in the business and any existing contracts over to the new business structure; and (ii) to get new licenses or permits (as licenses and permits usually cannot be transferred). 
You should seek the advice of the agency issuing the licenses or permits on their validity and seek professional advice generally if you are uncertain as to what should be done. 
At the point of submission of the online transaction to incorporate the company, you may indicate in the online form that the company is going to take over the business of the registered business (that is, the sole proprietorship or partnership). You are required to provide the details of the registered business (that is, the sole proprietorship or partnership) as well as the date of termination of the business (which can be postdated up to 3 months). Thereafter you will have to submit an online transaction to terminate the business registration (that is, notify ACRA that you have ceased to carry on business). The fee payable is $20. The fee payable to incorporate the new company is $315.