The following six years included frequent performances as soloist with the Symphonic Orchestra, and as recitalist at venues such as the National Academy of Arts and Letters, Liceo and Ateneo de Matanzas, the Medical Federation of Cuba, and other prestigious cultural societies throughout the island.

Though obviously a successful performer, a chance encounter at about this time with the great Russian cellist Gregor Piatigorsky resulted in a challenge for her to pursue a higher degree of technical mastery with the suggestion that she study in New York City with the incomparable Josef Lhévinne.

Upon her return to Cuba in 1941, she founded in the Vedado district of Havana the Instituto de Arte Musical, Arminda Schutte, which received national academic accreditation by the Ministry of Education for the conferral of degrees, certificates and diplomas.

Given the arrival of Communism in the island, she left Cuba in 1963 with her widowed mother via Mexico with the goal of seeking political asylum in the United States.

After a short stay in Mexico City, Schutte and her mother settled in Miami, Florida, near her younger brother, José Antonio and his family.

She first stayed with family, but subsequently Schutte moved out on her own, purchased a small home, studied English, and began teaching private lessons, depending initially on her reputation within the large Cuban community.

Schutte administered a thorough theoretical grounding to her pupils and used Théorie de la Musique by A. Danhauser as a framework, supplemented by other intervallic, scalar and harmonic studies.

Pupils were also trained in the European tradition of fixed-do Solfège (still used at The Juilliard School and at the Curtis Institute) for application in sight-singing and transposition at sight.

The principles of the Russian school of technique as received from the Lhévinnes was taught, from the most fundamental posture, shape and movements of the hands, fingers and wrist, to the most advanced aspects using a systematic review of mechanical exercises (Schmitt, Isidor Philipp, Theodor Kullak, Hermann Berens, Ignaz Moscheles), and études (Carl Czerny, Cramer, Muzio Clementi, Chopin and others).