"Thus it is with the truly righteous man. He is unconscious of his goodness and piety. Religious principle has become the spring of his life and conduct, and it is just as natural for him to bear the fruits of the Spirit as for the fig tree to bear figs or for the rosebush to yield roses. His nature is so thoroughly imbued with love for God and his fellow men that he works the works of Christ with a willing heart. SL 13.1"
"Wherefore by their fruits ye shall know them."
Both passages connect righteous living with producing good 'fruit.' Matthew 7:20 states that we will know people by their fruits, and the EGW passage uses the analogy of fruit trees to describe how a righteous person naturally produces good works.
"But the fruit of the Spirit is love, joy, peace, longsuffering, gentleness, goodness, faith, Meekness, temperance: against such there is no law."
The EGW passage speaks of bearing the 'fruits of the Spirit,' and Galatians 5:22-23 lists the specific attributes that constitute the fruit of the Spirit. The connection is clear and supports the idea that righteous living manifests in specific virtues.
"All who come within the sphere of his influence perceive the beauty and fragrance of his Christian life, while he himself is unconscious of it, for it is in harmony with his habits and inclinations. He prays for divine light, and loves to walk in that light. It is his meat and drink to do the will of his heavenly Father. His life is hid with Christ in God; yet he does not boast of this, nor seem conscious of it. God smiles upon the humble and lowly ones who follow closely in the footsteps of the Master. Angels are attracted to them, and love to linger about their path. They may be passed by as unworthy of notice by those who claim exalted attainments and who delight in making prominent their good works, but heavenly angels bend lovingly over them and are as a wall of fire round about them. SL 13.2"
"Let your light so shine before men, that they may see your good works, and glorify your Father which is in heaven."
Both passages discuss the outward manifestation of inner faith. Matthew 5:16 calls for good works to be visible, while the EGW passage describes how a Christian life's beauty and fragrance are perceived by others, even unconsciously. The connection is thematic, focusing on the impact of a righteous life on those around them.