Srila Prabhupada is a direct manifestation of Lord Caitanya, like Nityananda Prabhu is.
“Tat-prakāśān indicates the direct manifestation of the Supreme Personality of Godhead, Nityānanda Prabhu, and the initiating spiritual master.”
(Cc Adi 1.34p)
“Every living entity is essentially a servant of the Supreme Personality of Godhead, and the spiritual master is also His servant. Still, the spiritual master is a direct manifestation of the Lord. With this conviction, a disciple can advance in Kṛṣṇa consciousness. The spiritual master is nondifferent from Kṛṣṇa because he is a manifestation of Kṛṣṇa.”
(Cc Adi 1.44p)
“According to the deliberate opinion of all revealed scriptures, the spiritual master is nondifferent from Kṛṣṇa. Lord Kṛṣṇa in the form of the spiritual master delivers His devotees.”
(Cc Adi 1.45)
“Only out of His immense compassion does the Personality of Godhead reveal Himself as the spiritual master. Therefore in the dealings of an ācārya there are no activities but those of transcendental loving service to the Lord. He is the Supreme Personality of Servitor Godhead. It is worthwhile to take shelter of such a steady devotee, who is called āśraya-vigraha, or the manifestation or form of the Lord of whom one must take shelter. ….The bona fide spiritual master always engages in unalloyed devotional service to the Supreme Personality of Godhead. By this test he is known to be a direct manifestation of the Lord and a genuine representative of Śrī Nityānanda Prabhu. Such a spiritual master is known as ācāryadeva.”
(Cc Adi 1.46p)
Both Nityananda Prabhu and the Initiating Spiritual master are Servitor God.
“Śrī Balarāma is the servitor Godhead who serves Lord Kṛṣṇa in all affairs of existence and knowledge. Lord Nityānanda Prabhu, who is the same servitor Godhead, Balarāma, performs the same service to Lord Gaurāńga by constant association.”
(Cc Adi 5.10p)
Only out of His immense compassion does the Personality of Godhead reveal Himself as the spiritual master.
“Therefore in the dealings of an ācārya there are no activities but those of transcendental loving service to the Lord. He is the Supreme Personality of Servitor Godhead.”
(Cc Adi 1.46p)
“The jīva-tattva servitor, the spiritual master, is actually the servitor God. As explained in previous verses, in the absolute world there are no such differences, yet one must observe these differences in order to distinguish the Supreme from His subordinates.”
(Cc Adi 7.14p)
Hence, Srila Prabhupada, as a servitor God, a direct manifestation of the Supreme Lord, can also expand and take different forms to accomplish his services given by Lord Caitanya and His Divine Grace Srila Bhaktisiddhanta Saraswati Thakur Prabhupada—to publish books, preach all over the world, train disciples, and reciprocate with conditioned souls—just like Lord Caitanya does in three features.
bhakte kṛpā karena prabhu e-tina svarūpe
‘sākṣāt,’ ‘āveśa’ āra ‘āvirbhāva’-rūpe
SYNONYMS
bhakte—unto devotees; kṛpā—mercy; karena—bestows; prabhu—Lord Caitanya; e—these; tina—three; svarūpe—features; sākṣāt—directly; āveśa—empowered by the Lord; āra—and; āvirbhāva—appearance; rūpe—in the features.
TRANSLATION
Lord Śrī Caitanya Mahāprabhu bestows His causeless mercy upon His devotees in three features: His own direct appearance [sākṣāt], His prowess within someone He empowers [āveśa], and His manifestation [āvirbhāva].
PURPORT
The sākṣāt feature of Śrī Caitanya Mahāprabhu is His personal presence. Āveśa refers to invested power, like that invested in Nakula Brahmacārī. Āvirbhāva is a manifestation of the Lord that appears even though He is personally not present.
For example, Śrī Śacīmātā offered food at home to Śrī Caitanya Mahāprabhu although He was far away in Jagannātha Purī, and when she opened her eyes after offering the food she saw that it had actually been eaten by Śrī Caitanya Mahāprabhu. Similarly, when Śrīvāsa Ṭhākura performed saṅkīrtana, everyone felt the presence of Śrī Caitanya Mahāprabhu, even in His absence. This is another example of āvirbhāva. [56]
The appearance of Lord Śrī Caitanya Mahāprabhu in every devotee’s presence is called sākṣāt. His appearance in Nakula Brahmacārī as a symptom of special prowess is an example of āveśa. [57]
The former Pradyumna Brahmacārī was given the name Nṛsiṁhānanda Brahmacārī by Śrī Caitanya Mahāprabhu.[58]
In his body there were symptoms of āvirbhāva. Such appearances are uncommon, but Lord Caitanya Mahāprabhudisplayed many such pastimes through His different features. [59]
PURPORT
In the Gaura-gaṇoddeśa-dīpikā (74) it is said that Nakula Brahmacārī displayed the prowess (āveśa) and Pradyumna Brahmacārī the appearance (āvirbhāva) of Śrī Caitanya Mahāprabhu. There are many hundreds and thousands of devotees of Lord Caitanya among whom there are no special symptoms, but when a devotee of Lord Śrī Caitanya Mahāprabhu functions with specific prowess, he displays the feature called āveśa. Śrī Caitanya Mahāprabhu personally spread the saṅkīrtana movement, and He advised all the inhabitants of Bhāratavarṣa to take up His cult and preach it all over the world. The visible bodily symptoms of devotees who follow such instructions are called āveśa. Śrīla Śivānanda Sena observed such āveśa symptoms in Nakula Brahmacārī, who displayed symptoms exactly like those of Śrī Caitanya Mahāprabhu. The Caitanya-caritāmṛta states that in the Age of Kali the only spiritual function is to broadcast the holy name of the Lord, but this function can be performed only by one who is actually empowered by Lord Kṛṣṇa. The process by which a devotee is thus empowered is called āveśa, or sometimes it is called śakty-āveśa.[59]
Śrīla Śivānanda Sena experienced the three features sākṣāt, āveśa and āvirbhāva. Later I shall vividly describe this transcendentally blissful subject.[60]
(Cc Adi 10.56-60)
The question is often raised: How can Srila Prabhupada still guide disciples after his disappearance when “one cannot visually experience” him?
“Since one cannot visually experience the presence of the Supersoul, He appears before us as a liberated devotee. Such a spiritual master is none other than Kṛṣṇa Himself.”
(Cc Adi 1.58)
By expanding himself into various Vapuh forms (sākṣāt-personal presence) and manifested forms (Āvirbhāva – manifestation ..even though He is personally not present), he can be “visually experienced.”
As he equates himself with ISKCON as a branch of Lord Caitanya Tree, we have earlier surmised that he has expanded himself into ISKCON form which is another of his Vapuh forms.