To debug my solution I done this way.
In ProjectAPI.proj
<Project>
...
<PropertyGroup Condition="'$(Configuration)' == 'Debug'">
<TypeScriptTarget>ES5</TypeScriptTarget>
<TypeScriptIncludeComments>true</TypeScriptIncludeComments>
<TypeScriptSourceMap>true</TypeScriptSourceMap>
<TypeScriptOutFile>js\Base.js</TypeScriptOutFile>
<TypeScriptModuleKind>none</TypeScriptModuleKind>
<TypeScriptSourceRoot>$(ProjectDir)js/</TypeScriptSourceRoot>
<TypeScriptMapRoot>$(ProjectDir)js/</TypeScriptMapRoot>
</PropertyGroup>
<PropertyGroup>
<PostBuildEvent>
if $(ConfigurationName)==Debug copy "$(ProjectDir)js\Base.js" "$(ProjectDir)..\..\..\Shared\"
if $(ConfigurationName)==Debug copy "$(ProjectDir)js\Base.js.map" "$(ProjectDir)..\..\..\Shared\"
</PostBuildEvent>
</PropertyGroup>
</Project>
In PojectWebSite.proj
<Project>
...
<PropertyGroup>
<PreBuildEvent>
if $(ConfigurationName)==Debug copy "$(ProjectDir)..\..\..\Shared\Base.js" "$(ProjectDir)js\"
if $(ConfigurationName)==Debug copy "$(ProjectDir)..\..\..\Shared\Base.js.map" "$(ProjectDir)js\"
</PreBuildEvent>
</PropertyGroup>
</Project>
TypeScriptMapRoot was the secret to discover.