Can I transfer my CINPF to my employer's provident fund?

This is a question of company policy, the Fund rules and your employment contract. If the Fund rules and your employment contract stipulate that you must belong to the CINPF, then you have little choice in the matter (although you can lobby to have the fund rules and the contract terms changed). Some companies - offering multiple retirement funds - do allow employees falling within the same employment category to choose the fund they want to belong to. However, you then typically make that choice upfront, and you cannot change your mind later. But given the issues surrounding the CINPF at present, and subject to the fund rules, your employer could choose to give employees a once-off opportunity to switch between the two funds. Again, you would have to lobby for that.