Understand the concept of gift deed.
A gift is the transfer of existing movable or immovable property by a donor (the person making the gift) to a donee (recipient) and accepted by or on behalf of the donee. The gift of movable or immovable property must be in accordance with section 122 of the Transfer of Property Act, 1882.
Section 122 in The Transfer of Property Act, 1882
122. “Gift” defined.—“Gift” is the transfer of certain existing movable or immovable property made voluntarily and without consideration, by one person, called the donor, to another, called the donee, and accepted by or on behalf of the donee. Acceptance when to be made.—Such acceptance must be made during the lifetime of the donor and while he is still capable of giving. If the donee dies before acceptance, the gift is void.
No gift deed is required to be executed for gift of a movable property. Therefore, a simple letter of making the gift by the donor and a letter from the donee accepting such gift should be sufficient for the gift of a movable property.
Section 10 in The Transfer of Property Act, 1882
10. Condition restraining alienation.—Where property is transferred subject to a condition or limitation absolutely restraining the transferee or any person claiming under him from parting with or disposing of his interest in the property, the condition or limitation is void, except in the case of a lease where the condition is for the benefit of the lessor or those claiming under him: provided that property may be transferred to or for the benefit of a women (not being a Hindu, Muhammadan or Buddhist), so that she shall not have power during her marriage to transfer or charge the same or her beneficial interest therein.
Section 12 in The Transfer of Property Act, 1882
12. Condition making interest determinable on insolvency or attempted alienation.—Where property is transferred subject to a condition or limitation making any interest therein, reserved or given to or for the benefit of any person, to cease on his becoming insolvent or endeavoring to transfer or dispose of the same, such condition or limitation is void. Nothing in this section applies to a condition in a lease for the benefit of the lessor or those claiming under him.
The above are few provisions given in your interest.
You should understand the concept that a person can gift an item to another only when he is the owner of the item being gifted.
If your father is the absolute owner of the property and there can be no dispute about his ownership to this movable property there can be no legal infirmity to transfer this movable property by a gift deed subject to the provisions of law as mentioned in the above paragraphs.