The Boston Innovation Center is the first sign of life within the 23-acre Seaport Square mixed-use development in the Hub’s Innovation District as construction nears completion. Boston Global Investors and Morgan Stanley (NYSE: MS) donated $7 million for the center as part of mitigation for Seaport Square, a mixed-use development that promises to include a 6.3- million-square-foot neighborhood on 23 acres with apartments, offices, shops, a hotel and parks. The center, set for a spring grand opening,…