Yes . Partly-paid up shares can be transferred .
In such cases , Where the application is made by the transferor and relates to partly paid-up shares, the company has to give due notice of the amount due on shares/debentures to the transferee and the transferee shall raise objection, if any within two weeks from the date of receipt of the said notice.
Where the application is made by the transferor and relates to partly paid shares, the transfer shall not be registered, unless the company gives notice of the application to the transferee and the transferee makes no objection to the transfer within two weeks from the receipt of the notice. The notice to the transferee shall be deemed to have been duly given if it is dispatched by prepaid registered post to the transferee at the address given in the instrument of transfer, and shall be deemed to have been duly delivered at the time at which it would have been delivered in the ordinary course of post.
Please note that the transferee may be asked to pay the balance amount in the partly-paid-up share of the company.