Later works include Almindeligt Hospital in Amaliegade which he completed to designs by Nicolas-Henri Jardin in 1760 (demolished in 1892) and maintenance work both on Kongens Bryghus and Børsen (1779).
He moved to Denmark in 1739 where he was accepted into the masons" guild in 1740. In the beginning of his career, Conradi worked as a mason and builder. His first major work as such was Ledreborg (1743-1745).
In the late 1740s he began routinely working for Niels Eigtved, architect to the Royal Court, executing projects such as the first Royal Danish Theatre at Kongens Nytorv (1748-1749, demolished in 1874), Danish Asia Company"s warehouse at Asiatisk Plads (1748-1750), Christian"s Church (1755-1764) and the Lindencrone Mansion in Bredgade (1751).
From about 1750, Conradi increasingly also worked as an architect, designing the buildings that he built. Many of Conradi"s works are found in the Christianshavn neighbourhood.
These include two houses at 50–52 Prinsessegade (1750), the Royal Bording School, now known as Søkvæsthuset (1753-1755, later altered and expanded). the Wilder Warehouse at Wilders Plads (1762-1763) and Royal Greenland"s warehouse at Grøndlandske Handels Palds (now North Atlantic House. from 1764. His own house at Christianshavn Canal (29 Overgaden neden Vandet, 1752) and his rectory for Christian"s Church have both been demolished.
In Frederiksstaden, Conradi has built the house on the corner of Amaliegade (Number 19) and Fredericiagade (Number 2).
Among the buildings which are attributed to Conradi are Sæbygård in the west of Zealand (1740s, demolished), Christiansholm at Klampenborg (c 1748), Kaalund Convent (originally a farm under Kalundborg Castle, 1751-1752), 40–42 Amaliegade in Copenhagen (1756-1760) and Store Godthåb in Frederiksberg (1770). In 1783, Conradi acquired the property Bakkegården in Valby with plans to run it as an inn. He expanded the building (from then on known as Gammel Bakkehus, "Old Hill House") and built a new house (Ny Bakkehus, "New Hill House", now demolished) on a neighbouring site in 1764.
In 1766 he obtained a royal privilege to open the inn.
lieutenant was sold at auction when he went bankrupt in 1777.