Yes, you can convert the Term life policy into any permanent life policy.
If I convert to a permanent life policy, will I get an inferior product?
No, you can choose any available permanent life product available at the time of conversion. More importantly, you don't have to go through underwriting again, which means even your health situation deteriorates, you can keep the same Term life's underwriting class.
How much coverage can I have?
You can convert to up to the same Term life face amount. For example, if you have an $1 million Term life, you can convert to up to $1 million permanent life coverage. If you want more coverage, you will be subject to underwriting at the time of conversion.