Outdoor-to-indoor communications in millimeter-wave (mmWave) cellular networks have been one challenging research problem due to the severe attenuation and the high penetration loss caused by the propagation characteristics of mmWave signals. We propose a viable solution to implement the outdoor-to-indoor mmWave communication system with the aid of an active intelligent transmitting surface (active-ITS), where the active-ITS allows the incoming signal from an outdoor base station (BS) to pass through the surface and be received by the indoor user-equipments (UEs) after shifting its phase and magnifying its amplitude. Then, the problem of joint precoding of the BS and active-ITS is investigated to maximize the weighted sum-rate (WSR) of the communication system. An efficient block coordinate descent (BCD) based algorithm is developed to solve it with the suboptimal solutions in nearly closed-forms. In addition, to reduce the size and hardware cost of an active-ITS, we provide a block-amplifying architecture to partially remove the circuit components for power-amplifying, where multiple transmissive-type elements (TEs) in each block share a same power amplifier. Simulations indicate that active-ITS has the potential of achieving a given performance with much fewer TEs compared to the passive-ITS under the same total system power consumption, which makes it suitable for application to the size-limited and aesthetic-needed scenario, and the inevitable performance degradation caused by the block-amplifying architecture is acceptable.