No. Microsoft does not officially offer an adapter or conversion cable to connect a Surface Connect charger (Surface Pro 3 and later) to the original Surface Pro (1st Generation).
The two charging connectors are physically and electrically different.
The original Surface Pro uses Microsoft power supply Model 1536
Ref:
Surface charging requirements and power supplies for Surface Pro
Microsoft does not list a Surface Connect-to-original-Surface charging adapter in its supported accessories.
The recommended solution is to obtain the original 48W Surface power supply, Model 1536, designed for Surface Pro 1 and Surface Pro 2.